# What is the instantaneous rate of change of #f(x)=ln(4x^2+2x ) # at #x=-1 #?

##### 1 Answer

Jun 1, 2016

#### Explanation:

Instantaneous rate of change is simply the derivative. To find it, take the derivative of the function and evaluate it at the desired

We have a logarithmic function with a polynomial inside, which means we need to use the chain rule. As it applies the the natural log function, the chain rule is:

Where

In this case,

All that's left to find instantaneous rate of change is to evaluate this at