Explanation

We use the product rule since it's the product of two functions:

$$f(x) = x^3 cdot ln(x)$$

Let:

• $u = x^3 Rightarrow u' = 3x^2$

• $v = ln(x) Rightarrow v' = frac{1}{x}$

Apply the product rule:

f′(x)=u′v+uv′=3x^2⋅ln(x)+x^3⋅1/x​
f′(x)=3^x2ln(x)+x^2