# How do you find the derivative of f(x)=(x^2) + (3 ln x)?

Jun 20, 2015

The derivative of a sum is the sum of the derivatives and the derivative of a constant multiple of a function is the constant times the derivative of the function.

#### Explanation:

For $f \left(x\right) = \left({x}^{2}\right) + \left(3 \ln x\right)$, the derivative is:

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

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

$= 2 x + 3 \left(\frac{1}{x}\right)$

$= 2 x + \frac{3}{x}$ or, if you prefer a single ratio:

$= \frac{2 {x}^{2} + 3}{x}$