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

Let's perform the differentiation:

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

We differentiate

U1

x

and

V2

\ln (x)

using:

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

Let's perform the differentiation

U1

{(x)}^{'}

1

Let's differentiate

V2

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

\frac{1}{x}

You can evaluate the resulted derivative (

U1 \cdot V2

)':

1 \cdot \ln (x) + x \cdot \frac{1}{x}

▷Answer: $\ln (x) + 1$