Differentiate Definition and 227 Threads

Homework Statement Differentiate the following with respect to x leaving in the simplest form \frac{d}{{dx}}\left[ {\ln \left[ {\left( {1 - \sqrt x } \right)^2 \left( {1 + \sqrt x } \right)^3 } \right]} \right] Homework Equations The chain rule \frac{d}{{dx}}\left[ {\left( {f\left(...

x^2y the y is biglike the x its not small and how do you differentiate this xy^2 for the first one i used the product rule and thesecond one and i get a different answer then what i was suppost to get

y=x^2+4x+3/square root x i did this s x^2+4x+3) square root x/ sq x * sq x sq x *x^2)+4x*sq x+ 3/1

y=ex(x is suppost to be smaller and on the top right of e)/x squared i a suppost to differentiate this, well i wrote -2ex/x cubed+ ex/ x sq. now u probabl might be confused by the way i wrote it since i don't know how to put the right things for my problems, well i set up the problem...

...Kay, so I was doing [or trying to do] my homework, and it's pretty basic, actually. We're given a table comprising substances like "vegetable oil", "gatorade", "pencil lead", etc; and asked to predict its electrical conductivity. I tried Googling some of it, but nothing really relevant...

Could someone please make sure I'm doing this right. I want to find the derivative of the logarithm to the base a of x, using implicit differentiation. Let y = \log_{a} x a^y = x \frac{d}{dx} (a^y) = 1 (implicit differentiation) \frac{d}{dx} (e^{\ln a})^y = 1 \frac{d}{dx} (e^{(\ln a)y}) = 1...

Find the derivative. http://img65.imageshack.us/img65/232/der429bj.gif I really don't know which way to go with this.. It's just really complicated.

differentiate inverse tan (2x / [1 - x^2] ) with respect to inv sin ( 2x / [1 + x^2] ). may i know what does it mean with respect to inv sin and how to start wif this ques pls

I am to differentiate with respect to z, where a is independent of z... (am assuming that that a is a constant?) a. e^{a^2 z}=diff=>a^2 e^{a^2 z} b.e^{ia z}=cos(az)+isin(az)=diff=>-sin(az)+icos(az) c. (e^{-i z})^2=cos(2z)-isin(2z)=diff=>-sin(2z)-icos(2z) d...

I'm a little confused as to when to stop taking the derivative of the inside function when using the chain rule... Lets say I have f( g(x^2) ) Would this be correct? f`( g(x^2) ) * g`(x^2) * 2x ? Or do I keep on going until the x is completely gone from the equation?

I know this is how to differentiate a funtion consisting of two terms: f(x)=xy , f'(x)=x'y+y'x But is this how to differentiate three terms: f(x)=xyz , f'(x)=(x'y+y'x)+(y'z+z'y)+(x'z+z'x) :confused:

How? I know that a scalar quantity only comprises of magnitude while a vector consist of both magnitude and direction.. But is there no definite formula to determine whether or not a quantity is a scalar or a vector.. or is there a list of scalars and vectors to show all quantities...

Hi, I am having a bit of trouble, i am getting ready for an exam, one the questions i have asks "given the curve y = e^x, draw tangents to esitmate the gradients of the curve when a)x=0, b)x=1, c)x=-1, Now i know the answers are: a) 1 b) 7.39 c)0.05 However the toruble i am...

I wonder if this can be differentiated ,if it can then what is the derivative of [x^x^x^x^x^x...]^[(x^2)^(x^2)^(x^2)...]^[(x^3)^(x^3)^(x^3)...]^[(x^4)^(x^5)...]...... thank you

how do u differentiate f(x)=│x^2-4│...? i don't know how to do it with absolute values...

differentiate 2x/(x+y)=y Method1: 2x=xy+y^2 d/dx(2x)=d/dx(xy+y^2) 2=y+xy'+2y(y') y'=(2-y)/(x+2y) Method2: 2x/(x + y) = y y' = [2(x + y) - (2x)(1 + y')]/(x + y)^2 [(x + y)^2 + 2x]y' = 2(x + y) - 2x y' = 2y/[(x + y)^2 + 2x] Which method is using "implicit" differentiation?

how to differentiate between the two masses in equation for relativistic mass? m= mo/sqroot 1-v^2/c^2 what's the difference between m and mo? and what about for energy: eo and e?

$ 4xy = y^2 + 2 \ln x How do I differentiate that?

Find dy/dx. x^5 log_{2}y-10 = 0 Differentiate both sides with respect to x. 5x^4 log_{2}y + x^5/ (y ln2) dy/dx = 0 dy/dx = -50y ln2 / x^6 Is it correct? please tell me..

Take this double replacement reaction for example: Na_2SO_4 + CaCl_2 How am I supposed to tell whether the product will be CaSO_4 + Na_2Cl_2 or CaSO_4 + 2NaCl? Obviously, there's a difference between Calcium Sulfate + 2 Sodium Chloride molecules and Calcium Sulfate + Sodium DiChloride...

v=vi*e^(-ct) The question asks to differentiate that equation for v(t) and thus show that the acceleration is porportional to the speed at any time. I have no clue how to differentiate. Could someone start me off or give some clues? I'll find th rest in my textbook. Thanks

can anybody differentiate this to simplest form y=4/3+5cosx

Do i just use the chain rule to differentiate 3^2x

f(x) = x.e^(-pi.x^2) this is how I tried to do it... f'(x) = x.(-pi.2.x.e^(-pi.x^2)) + 1.e^(-pi.x^2) f'(x) = (1 - 2.pi.x^2).e^(-pi.x^2) can anyone see anything wrong with this? Cheers

x^2 - xy - y^2 = 3 how do i work out dy/dx?

I'm not sure how to do this one. Only way I can think of is using the Product Rule but I don't know how to apply it when there are more than two functions. Something like: y=(x)(sinx)(cosx) --separate it into three different functions-- f(x)=x, g(x)=sinx, z(x)=cosx --use Product...

can someone differentiate e^(nx) where n is any integer. i think is equal to n*e^(nx). please show the proof, thanx. :smile: :smile: :smile: