a. Use the Product Rule to find the derivative of the given function b. Find the

Question

a. Use the Product Rule to find the derivative of the given function b. Find the derivative by expanding the product first. f(x) (x 4)(2x +1) a. Use the product rule to find e derivative of the function. Select the correct answer b O A. The derivative is ( (x-4) O B. The derivative is (x(2x+ 1) O C. The derivative is (x-4)2x+1)+(D 0 D. The derivative is (x-4)(2x+1)CD OE, The derivative is (x-4)CD+(2x+1)(E) b. Expand the product (x-4)(2x + 1)-L] (Simplify your answer.) Using either approach. dr (x-4)2x + 1 Click to select your answer(s)

Explanation / Answer

a. f(x)=(x-4)(2x+1)

product rule (u v) ' = u'v +u v'

Here u= x-4,u'=1

v=2x+1,v'=2

so we get

f'(x)= 1(2x+1)+(x-4)2= 2x+1+2x-8=4x-7

b. f(x)=(x-4)(2x+1)= 2x2-7x -4

f'(x)=2(2x)-7(1)= 4x-7

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