Differentiate Definition and 227 Threads

Hi, this is my online homework exercise. I think I did it right, but the system gives me wrong answer... Can someone please check what I did y=$\sqrt{x+\sqrt{x+\sqrt{x}}}$...

they have different names or something else?

Is it possible to differentiate xa+bi where a and b are real ? if so what is the answer ?

Homework Statement Hi Everyone, This seems like a very simple question but I' a bit confused. In maths if I wanted to differentiate y = x^2 then it would just be 2x but I'm not sure about what you would do in physics. If you had the equation C = m/V (Concentration = mass/volume) how can you...

Homework Statement find points where function is differentiable http://puu.sh/cqrc8/f96bd06aee.png Homework Equations H(x) = 1, x >= 0 H(x) = 0, x < 0[/B] The Attempt at a Solution i Draw a number line and see where the function would change or jump. and immediately i noticed that the...

Homework Statement Find the slope to the tangent line to the polar curve r^2 = 9 sin (3θ) at the point (3, π/6) Homework Equations dy/dx = (r cos θ + sin θ dr/dθ)/(-r sin θ + cos θ dr/dθ) The Attempt at a Solution So I have no issues with taking r^2 = 9 sin (3θ) and taking the...

Can someone guide me with the steps to differentiate a geometric sum, x? ^{n}_{i=0}\sumx^{i}=\frac{1-x^{n+i}}{1-x} If I'm not wrong, the summation means: = x^0 + x^1 + x^2 + x^3 + ... + n^i Problem is: I have basic knowledge on differentiating a normal numbers but how do I apply...

Definition/Summary The trick is to change a difficult integral into an easier integral by treating a constant as a variable, and integrating with respect to that variable first. For example, in normalising Gaussians, the difficult integrand x^2 \exp ( - \lambda x^2) where \lambda is a...

Homework Statement Using the function of a function formula differentiate the following: y = (cos 2x)3 Homework Equations dy/dx = dy/du * du/dx The Attempt at a Solution y = (cos 2x)3 u = cos 2x y = u3 dy/du = -2sin2x du/dy = 3u2 dy/dx = dy/du * du/dx dy/dx =...

Hi Ive got some calculations to do on amount of charge on a capacitor with respect to t. Formula for amount of charge on a capacitor is Q=5.7ln4.5t I need to determine the rate of discharge with different values of t, t=5ms t=7.5ms I know i need to differentiate the formula...

Homework Statement 12.5 sin(0.06 t) What rule would I use to differentiate it? Homework Equations - The Attempt at a Solution Chain rule?

Homework Statement Differentiate the function ##f(x)=\sqrt{x}## The Attempt at a Solution Power rule: $$\sqrt{x}=x^{\frac{1}{2}}$$ $$\frac{d}{dx}x^{\frac{1}{2}}=\frac{1}{2}x^{-\frac{1}{2}}$$ This is simple.However,I want to solve it using the definition of the derivative $$\lim_{\Delta x \to...

Okay i got how to do x1/3 by using the difference of cubes and x1/2 by difference of squares but I am stuck on what todo with x1/6. what i tried so far F(x)= [ f(x+h) - f(x) ]/ h a2= (x+h)1/6 b2= (x)1/6 so I eventually got to [a6-b6]/h[a4+a2b2+b4 I used the difference of cubes with this or...

I seem to not be able to differentiate between the two of these phenomenons. Please give me some example in daily life to show the difference between them.

Is it possible to differentiate a scalar( in this case a Lagrangian) by a vector ? If the Lagrangian is r.A ie. the scalar product of vectors r and A what is ∂L/∂r ? My notes say it is A but how ? My notes also say that ∂L/∂r is the same as ∇L. Is this correct ? or is it sloppy notation ? or...

Homework Statement Differentiate from first principles with respect to x: x^n (where n belongs to the natural numbers). Homework Equations f'(x) = Lim x→0 [f(x+h) - f(x)]/h The Attempt at a Solution f'(x) = Lim x→0 [f(x+h) - f(x)]/h = Lim x→0 [(x+h)^n - x^n]/h I need some...

Homework Statement Differentiate (x+1)^1/2 from first principles with respect to x. Homework Equations f'(x) = Lim h→0 [f(x+h) - f(x)]/h The Attempt at a Solution f'(x) = Lim h→0 [f(x+h) - f(x)]/h f'(x) = Lim h→0 [(x+h+1)^1/2 - (x+1)^1/2]/h I'm unsure how to simplify from there.

1. The problem statement Differentiate with respect to (x) the following function... https://www.physicsforums.com/attachment.php?attachmentid=62329&stc=1&d=1380565485 *As you can see I attempted logarithmic differentiation but am unsure if I'm doing it right at the moment. Could someone...

Homework Statement Differentiate: Homework Equations y=∛((7-3x^2)^2) The Attempt at a Solution y^'(x)=(4x(3x^2-7))/(∛((7-3x^2 )^2))^2 )

Hello MHB, I am working with finding max and min value and I always hesitate when I got absolute value so the one I strugle is to derivate |\sin(x+y)| if we do it respect to x is this correct? f_x(x,y)=\frac{\sin(2x)}{2\sqrt{\sin^2(x+y)}}|\pi\rangle

Homework Statement Differentiate f(x) = x^{1/2} - x^{1/3} Homework Equations f(x) = f'(x)- g'(x) The Attempt at a Solution I am a little stuck about what to do after the first couple steps. Here is my attempt. f(x) = x^{1/2} - x^{1/3} f'(x) = (x^{1/2})' -(x^{1/3})' =...

Homework Statement Differentiate f(x) = (x^2 - 3x)^2 Homework Equations f'(x) = nf'(x)f(x)^(n-1) The Attempt at a Solution f’(x) = 2(x2-3x)’(x2-3x)2-1 = 2(2x-3)(x2-3x)1 = 2(2x3 – 6x2 – 3x2 + 9x) = 2(2x3 – 9x2 + 9x) = 4x3 – 18x2+ 18x Is this correct?

Differentiate the function: $\frac{1+\ln(t)}{1-\ln(t)}$ Is this correct? $\frac{1/t(1-\ln(t))-(-1/t)(1+\ln(t))}{(1-\ln(t))^2}$ I got none facit in My textbook so I would like to someone confirmed I am doing right.

I find that I don't have the symbolic toolbox. Due to this, I'm not being able to differentiate by using the usual 'diff' command. However, just as one can integrate numerically, by using the quad and quadl functions, is there no way to differentiate numerically on MATLAB (like using the ab...

Homework Statement (1-2x3+x2)((1/x3)+1) Homework Equations f'g(x)+g'f(x) f'(x)=-6x3+2x g'(x)=(-1/x4) The Attempt at a Solution I found what i believe to be the derivative of both f(x) & g(x) and used the product rule to get to where I am stuck right now: [(-6x2+2x)(1/x3)]+[(-1/x4)(1-2x3+x2)

How do you differentiate kirchhoffs law which seems to be I = (R+L(di/dt))/V(t) I need it to be a differential equation so then I can use eulers method.

Homework Statement 2^{Sin(PiX)} Homework Equations The Attempt at a Solution = e^{(Sin(\PiX})ln2 y'= e^{(Sin(\PiX})ln2 d/dx [Sin \PiX] ln 2 and I'm stuck... The product rule will automatically lead to to differentiating ln 2.

I am in Calculus 2 and we're just reviewing calc 1. Can someone break down the concept of differentiating definite integrals for me? I am mostly struggling on the trig functions. The problem I am stuck on is ∫^{}x_{}0 cos(t^{}2) dt

1. Find derivative: g(x) = (e^x)/(2 + 3x)2. The fraction confuses me... I wrote it instead as: (e^x)(3x^-1)(2^-1) 2^(-1) equals .5, so then I thought it was: (e^x)(1.5x^-1) And then I thought it's time to differentiate... So I got: (-1.5x^-2)(e^x) And then I thought, " Since these are...

Homework Statement Differentiate s = Tan ^{2}(e^{4t}) Homework Equations [e^{u}]' = u' e^{u} [Tan(θ)]' = Sec^{2}(θ) Sec(θ) = \frac{1}{Cos(θ)} The Attempt at a Solution s' = 2[Tan(e^{4t})] * Sec^{2}(e^{4t}) * 4e^{4t} s' = 8e^{4t} * Tan(e^{4t}) * Sec^{2}(e^{4t})...

I need help to take the time derivative of a physics equation. The equation: ME=1/2 mr^2 (dθ/dt)^2 +mgr θ^2/2 Where ME is the mechanical energy , m is the mass of the object, r is the radius of the path of the object and θ is the angle around the path. Walter Lewin at MIT...

1. Differentiate 2. y = \frac{v^{3} - 2v\sqrt{v}}{v} 3. I am trying to use the quotient rule, but am having trouble understanding how to use the square root. Here's what I have \frac{v(3v^{2}-2*1/2\sqrt{v}) - v^{3}+2v*1/2\sqrt{v}}{v^{2}}

I was wondering how (or if it is known) the Higgs assigns different masses to different particles. We know that mass comes from the resistance that the Higgs field provides to particles but why are some particles such as photons able to move through without a hint of resistance, whereas...

Homework Statement Lim (cosθ-√3/2)/(θ-pi/6) θ→pi/6 Homework Equations The Attempt at a Solution My attempt at this has been to try to multiply both the numerator and denominator by either the numerator's or denominator's conjugate. both result in 0 at the denominator. I also...

Homework Statement Someone has written down in some notes about differentiating DeBroglies Theorem. They've started with Px =h/λ (That's P sub x) Then they've simply said, this differentiated is: ΔPx = [-h/(λ^2)]Δλ How have they done this? What method? What have they...

Homework Statement A ball is thrown with an angle of 45 degrees to the horizontal by a person standing on the ground. The y-component of the velocity of ball in projectile motion is differentiated with respect to time. i.e. dv/dt of the y-component of velocity.Homework Equations The Attempt at...

Homework Statement Differentiate x^(cosx) = y ^(sinx) with respect to x Homework Equations The Attempt at a Solution I tried using natural logs but I am not sure if its correct, if it's wrong please point me to the right direction, thanks x^(cosx) = y^(sinx) ln x^(cosx) = ln y ^(sinx) ln x...

Homework Statement \frac{∂ \frac{\vec{a}}{ \vec{a} . \vec{b}} }{∂\vec{a}} b is not a function of a Homework Equations I want to differentiate this, (the jacobian of the vector field) dot is the Euclidean inner product.The Attempt at a Solution \acute{u}.v -...

The definition of temperature is: 1/T = ∂S/∂U but mathematically this is a bit weird. Because S = klnW, where W denotes the multiplicity. And the multiplicity certainly does not form a continuous basis, but rather a set of spread out integers. So S must be a discrete function! Therefore my...

Homework Statement The Attempt at a Solution I really need some help here. I've been able to get through about 50 pages of calculus without really understanding what it means to differentiate both sides with respect to t, now I've run out of space to hide and I can't succeed any more without...

Homework Statement differentiate f(x)= x sin x Homework Equations The Attempt at a Solution The answer is x cos x + (sin x) * 1 I thought the derivative of sine was cosine. So why isn't the answer x cos x?

Homework Statement Consider three univariate distinct functions f_1(x),f_2(y),f_3(y). Let H be given by the following integral: H=\int_{0}^{f_1(x)} G(f2(\xi))G(f3(\xi))d\xi The Attempt at a Solution Then, computing dH/dy should give zero. However, I am not certain of this because...

Homework Statement Differentiate with respect to x y = tan^(-1) x Homework Equations The Attempt at a Solution ANSWER in book: y = tan^(-1) x x = tan y dx/dy = sec^(2) y = (1 + x^2) dy/dx = 1 / (1 + x^2) How is it known that sec^(2) y = (1 + x^2) Does it follow from an identity?

Homework Statement Differentiate -sin2x Homework Equations CHAIN RULE dy/dx=dz/dx*dy/dz PRODUCT RULE The Attempt at a Solution Using the chain rule; let z = -sinx let y = z2 dz/dx = -cosx dy/dz = 2z dy/dx=dz/dx*dy/dz = -cosx*2-sinx = 2cosx*sinx If I use the...

Homework Statement Given that ln(x) = y ln(a) find dy/dx Homework Equations The Attempt at a Solution So y = ln(x) / ln(a) thus we use the quotient rule ln(x) --> 1/x ln(a) --> 1/a Denominator = [ln(a)]2 So the differentiated equation is ln(a)/x - ln(x)/a...

Homework Statement y = 3*cube root 3√(x2-1) Homework Equations Udu/dx + Vdv/dx (wrong as per below) Chain Rule now used The Attempt at a Solution I have: Now y = 3*(x2-1)^1/3 let z=x2-1 y= 3(z)^1/3 dz/dx = 2x dy/dz = z^-2/3 = (x2-1)^-2/3...

Homework Statement If lny = sinh^(-1)(x), prove that (1+ x^2)y'' + xy' - y = 0 The attempt at a solution I have tried various (unsuccessful) ways of doing this, but the basic procedure that I've done is: D.w.r.t.x for lny = sinh^(-1)(x) This gives: (1/y)y' = 1/(1 + x^2) To...

Homework Statement Find the point on the graph of f(x)=√x that is closest to the value (4,0). (differentiate the square of the distance from a point (x,√x) on the graph of f to the point (4,0).) Homework Equations f(x)=√x The Attempt at a Solution Square of distance from (4,0)...

How do i differentiate something like 12/(x^+3)??2 I am acquainted with differentiating equations like (2x+5)^2 ( by chain rule and the direct method). But how do i go about with the equation 12/(x^2+3)? The specific doubt is that the answer given -12(x^2+3)^-2 into(multiplied by) 2x. I am...

Homework Statement I'm total newbie when it comes to differenciatiation, and was wondering if I'm doing this correct. Basically, this is a physics problem, but thought I'd put this in the calculus section for specific help. It's about a ball undergoing SHM, after being dropped down a...