# What is the derivative of  f(x) = 3x^2 ln 2x?

Nov 4, 2017

$\frac{d}{\mathrm{dx}} \left(3 {x}^{2} \ln 2 x\right) = 3 x \left(1 + 2 \ln 2 x\right)$

#### Explanation:

Using the product rule:

$\frac{d}{\mathrm{dx}} \left(3 {x}^{2} \ln 2 x\right) = \frac{d}{\mathrm{dx}} \left(3 {x}^{2}\right) \ln 2 x + 3 {x}^{2} \frac{d}{\mathrm{dx}} \left(\ln 2 x\right)$

$\frac{d}{\mathrm{dx}} \left(3 {x}^{2} \ln 2 x\right) = 6 x \ln 2 x + 3 {x}^{2} \frac{2}{2 x}$

$\frac{d}{\mathrm{dx}} \left(3 {x}^{2} \ln 2 x\right) = 6 x \ln 2 x + 3 x$

$\frac{d}{\mathrm{dx}} \left(3 {x}^{2} \ln 2 x\right) = 3 x \left(1 + 2 \ln 2 x\right)$