Question

Find the derivative of the function f(x) = 5(2 - x2)3

Answer 1

We will like to find the derivative of the function

`f(x)=5(2-x^2)^3`

then

`\begin{gathered} (df)/(dx)=(d)/(dx)\lbrack5(2-x^2)^3\rbrack \\ =5(d)/(dx)(2-x^2)^3 \\ =5\lbrack3(2-x^2)^2(d)/(dx)(2-x^2)\rbrack \\ =5\lbrack3(2-x^2)^2(-2x)\rbrack \\ =-30x(2-x^2)^2 \end{gathered}`

In this process we use the chain rule

`(d)/(dx)\lbrack f(x)\rbrack^n=n\lbrack f(x)\rbrack^(n-1)`

to find the derivative of

`(d)/(dx)(2-x^2)^3`

therefore

`(df)/(dx)=-30x(2-x^2)^2`