if f (x) = 2xsin x , then what is the slope of the tangent line to the graph of f (x) when x =π/2

Question

if f (x) = 2xsin x , then what is the slope of the tangent line to the graph of f (x) when x =π/2

A) 2

(B) 12

(C) 0

(D) π

Answer 1

This is a fairly straightforward problem that asks you to find a derivative and evaluate it at a specific point.

Since f(x) = g(x)h(x), we use the product rule, f'(x) = g'(x)h(x) + g(x)h'(x):

f'(x) = 2sin(x) + 2xcos(x) =>

f'(π/2) = 2 + 0 = 2, so the answer should be A,