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

User Sriharsha
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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

User Shawn Steward
by
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