# How do you differentiate #s(x)=log_3(x^2+5x)#?

##### 1 Answer

Jun 14, 2016

#### Explanation:

We can rewrite

#log_a(b)=log_c(b)/log_c(a)#

Here, we will choose a base of

#s(x)=ln(x^2+5x)/ln(3)#

When differentiating this, note that

To find the derivative of

Since

Thus:

#s^'(x)=1/ln(3)*1/(x^2+5x)*d/dx(x^2+5x)#

#s^'(x)=(2x+5)/((x^2+5x)ln(3))#