Question

1. Differentiate y = 2x cos x with respect to x​

Answer 1

2cosx - 2xsinx

Explanation:

Differentiate using the product rule

Given y = f(x)g(x), then

`(dy)/(dx)` = f(x)g'(x) + g(x)f'(x)

Here

f(x) = 2x ⇒ f'(x) = 2

g(x) = cos x ⇒ g'(x) = - sin x

Hence

y = 2x cos x

`(dy)/(dx)` = 2x(- sinx) + 2cosx = 2cos x - 2xsin x