# How do you find the derivative of 18lnx+x^2+5?

Apr 14, 2016

$\frac{18}{x} + 2 x$

#### Explanation:

Through the sum rule, to find this function's derivative, add each part's derivative to one another:

Thus, we just need to find the derivative of each part:

$\frac{d}{\mathrm{dx}} \left(18 \ln x\right) = 18 \frac{d}{\mathrm{dx}} \left(\ln x\right) = 18 \left(\frac{1}{x}\right) = \frac{18}{x}$

Recall that $\frac{d}{\mathrm{dx}} \left(\ln x\right) = \frac{1}{x}$, and that $18$ is just a constant being multiplied, which we can multiply by the derivative of $\ln x$.

Through the power rule, we see that

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

And, since $5$ is a constant,

$\frac{d}{\mathrm{dx}} \left(5\right) = 0$

Thus, the function's derivative is

18/x+2x+0" "=" "color(blue)(18/x+2x