Question

What is the derivative of (x + 1) sin x?

Answer 1

sin x + x · cos x + cos x

Explanation:

• (x + 1) = u → u' = 1
• sin x = v → v' = cos x

f(x) = u · v → f'(x) = u' · v + u · v'

f(x) = (x + 1) sin x

f'(x) = 1 · sin x + (x + 1) · cos x

f'(x) = sin x + x · cos x + cos x

Answer 2

`\boxed{\sf (d)/(dx)x^n=nx^(n-1)}`

`\boxed{\sf (d)/(dx)sinx=cosx}`

Now

`\\ \sf\longmapsto (d)/(dx)(x+1)sinx`

`\\ \sf\longmapsto 1+cosx`