Find the derivative of (t^2 - 4/t^4)*t^3

  • Thread starter carbz
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    Derivative
In summary, the first problem involves finding the derivative of (t^2-4/t^4)*t^3, which can be simplified to t^5+4t^-1. The second problem involves finding the derivative of (6x+5)(x^3-2)/(3x^2-5), which can be simplified to (18x^5-45x^3+10x^2+15x)/((3x^2-5)^2). Both solutions can be found using the product rule and simplifying the expressions.
  • #1
carbz
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I have two of these here...

Homework Statement


Find the derivative


Homework Equations


[tex](t^2-\frac{4}{t^4})*t^3[/tex]


The Attempt at a Solution


This is how far I got:
[tex](t^2-4t(^-4))(t(^3))[/tex]
[tex](t^2-4t(^-4))(3t(^2))+(t^3)(2t+16t(^-5))[/tex]


Homework Statement


Find the derivative


Homework Equations


[tex]f(x) = \frac{(6x+5)(x^3-2)}{(3x^2-5)}[/tex]


The Attempt at a Solution


This is what I got only:
[tex](6x+5)(x^3-2)(3x^2-5)(^-1)[/tex]
 
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  • #2
Well for [tex](t^2-\frac{4}{t^4})*t^3[/tex]

you could just multiply it out and get [tex]t^5+\frac{4}{t}=t^5+4t^{-1}[/tex] and proceed to differentiate w.r.t. t

for the 2nd one
[tex]\frac{d}{dx}(uv)=\frac{v\frac{du}{dx}+u\frac{dv}{dx}}{v^2}[/tex]

by that formula you should see that the end derivative would be a fraction
 
  • #3
always simplify from the beginning if you can

for 2. take the ln of both sides and expand it then take the derivative
 
  • #4
Allright, thanks. I got both problems worked out correctly now.
 

FAQ: Find the derivative of (t^2 - 4/t^4)*t^3

What is the formula for finding the derivative of a function?

The formula for finding the derivative of a function is dy/dx = lim(h->0) [(f(x+h) - f(x))/h], where f(x) is the given function and h represents an infinitely small change in the independent variable x.

How do you find the derivative of a product of two functions?

To find the derivative of a product of two functions, use the product rule which states that the derivative of a product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function. In other words, if f(x) and g(x) are two functions, then (f(x)*g(x))' = f(x)*g'(x) + g(x)*f'(x).

Can the quotient rule be used to find the derivative of a function?

Yes, the quotient rule can be used to find the derivative of a function. The quotient rule states that the derivative of a quotient of two functions is equal to the denominator times the derivative of the numerator, minus the numerator times the derivative of the denominator, all divided by the square of the denominator. In other words, if f(x) and g(x) are two functions, then (f(x)/g(x))' = (g(x)*f'(x) - f(x)*g'(x)) / (g(x)^2).

How do you find the derivative of a function with multiple terms?

To find the derivative of a function with multiple terms, use the sum rule which states that the derivative of a sum of two or more functions is equal to the sum of the derivatives of each individual function. In other words, if f(x) and g(x) are two functions, then (f(x) + g(x))' = f'(x) + g'(x).

How do you apply the chain rule to find the derivative of a composite function?

To apply the chain rule to find the derivative of a composite function, first identify the inner function and the outer function. Then, take the derivative of the outer function and multiply it by the derivative of the inner function. In other words, if f(x) and g(x) are two functions, then (f(g(x)))' = f'(g(x)) * g'(x).

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