Find the derivative of f(x)=(x^2+8)(8x-1) by first expanding the polynomials. Enter the fully simplified expression for f(x) after expanding the polynomials

Wevybrearttexcl 2022-09-17 Answered
Find the derivative of f ( x ) = ( x 2 + 8 ) ( 8 x 1 ) by first expanding the polynomials.
Enter the fully simplified expression for f (x) after expanding the polynomials
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Answers (1)

Emaidedip6g
Answered 2022-09-18 Author has 11 answers
f ( x ) = ( x 2 + 8 ) ( 8 x 1 )
find derivative=?
We use the substitutions u = x 2 + 8 and v=8x-1
Now, use product rule
d ( u v ) d x = u d v d x + v d u d x = ( x 2 + 8 ) d d x ( 8 x 1 ) + ( 8 x 1 ) d d x ( x 2 + 8 )
Now, we differentiate
= ( x 2 + 8 ) × ( 8 ) + ( 8 x 1 ) × ( 2 x ) = 8 x 2 + 64 + 16 x 2 2 x = 24 x 2 2 x + 64 f ( x ) = 24 x 2 2 x + 64
Now, find f'(x)=?
f ( x ) = 24 x 2 2 x + 64
differentiate with respect to x
f ( x ) = 48 x 2

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