differentiate x*sin(x) — step-by-step solution

Let's perform the differentiation:

{(x \cdot \sin (x))}^{'}

For

U1

x

and

V2

\sin (x)

, use the product/quotient rule:

{(U1 \cdot V2)}^{'} = {(U1)}^{'} \cdot V2 + U1 \cdot {(V2)}^{'}

Let's differentiate

U1

{(x)}^{'}

1

Let's perform the differentiation

V2

{(\sin (x))}^{'}

\cos (x)

You can evaluate the resulted derivative (

U1 \cdot V2

)':

1 \cdot \sin (x) + x \cdot \cos (x)

\sin (x) + x \cdot \cos (x)

▷Answer: $x \cdot \cos (x) + \sin (x)$