Chain Rule and Higher Order Derivatives. Find the derivative f(x)=(5x^{2}-2x+1)^{3}

hexacordoK

hexacordoK

Answered question

2021-04-23

Chain Rule and Higher Order Derivatives. Find the derivative
f(x)=(5x22x+1)3

Answer & Explanation

Adnaan Franks

Adnaan Franks

Skilled2021-04-25Added 92 answers

Step 1
the given function is:
f(x)=(5x22x+1)3
we have to find the derivative of the given function.
Step 2
f(x)=(5x22x+1)3
differentiating both the sides with respect to 'x' we get
ddxf(x)=ddx(5x22x+1)3
f(x)=3(5x22x+1)2×ddx(5x22x+1)
=3(5x22x+1)2(5ddx(x2)2d(x)dx+ddx(1))
=3(5x22x+1)2(5(2x)2(1)+0))
=3(5x22x+1)2(10x2)
therefore the derivative of the given function f(x)=(5x22x+1)3is 3(5x22x+1)2(10x2)

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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