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

Aug 22, 2015

You don't need it for this. There are no nonconstant functions multiplying.

$f ' \left(x\right) = \frac{d}{\mathrm{dx}} \left[f \left(x\right)\right] = \textcolor{b l u e}{2 x + \frac{3}{x}}$

using the power rule on ${x}^{2}$:

$\frac{d}{\mathrm{dx}} \left[{x}^{2}\right] = 2 \cdot {x}^{2 - 1} = 2 x$

and differentiating $\ln x$. You can float $3$ out of the derivative:

$\frac{d}{\mathrm{dx}} \left[3 \ln x\right] = 3 \frac{d}{\mathrm{dx}} \left[\ln x\right] = 3 \cdot \frac{1}{x} = \frac{3}{x}$