If , f(x) = 2x(sin x + cos x)

Question

If , f(x) = 2x(sin x + cos x) find

f′(5)

Answer 1

Use the product rule:

(u•v)' = u'v + uv'

where u = 2x and v = sin(x) + cos(x)

f'(x) = 2(sin(x) + cos(x)) + 2x(cos(x) - sin(x))

f'(5) = 2(sin(5) + cos(5)) + 2(5)(cos(5) - sin(5))

f'(5) ≈ 2(-0.959 + 0.284) + 10(0.284 + 0.959)

f'(5) ≈ 2(-0.675) + 10(1.243)

f'(5) ≈ 11.075

Answer 2

f(x) = 2x(sin x + cos x)

f'(x) = 2(sin x + cos x)+2x(cos x-sin x)

f'(5) = 2(sin 5 + cos 5)+10(cos5-sin5)= 12cos5-8sin5

If you like you can simplify further.