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Chapter 2: Q 10. (page 237)

Find the derivatives of the function:f(x)=x-1(4-x)2.

Short Answer

Expert verified

The derivative off(x)=x-1(4-x)2is1-4x2.

Step by step solution

01

Given information 

The given expression isf(x)=x-1(4-x)2.

02

Simplification  

f'(x)=ddx{f(x)}=ddx{x-1(4-x)2}=-1x2(4-x)2+1x.2(4-x).-1=-{16-8x+x2+2x(4-x)x2}=-16-8x+x2+8x-2x2x2=-16-x2x2=1-4x2Hence,f'(x)=1-4x2.

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