a Use the Product Rule to find the derivative of the given f

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)

Solution

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