# What is the derivative of #f(x)= 2^(3x)#?

##### 2 Answers

#### Explanation:

#### Explanation:

You may be tempted to differentiate this like it were

The good thing is, since finding the derivative of an exponential function with base

The first step is recognizing that the following is true:

#f(x)=2^(3x)=e^ln(2^(3x))#

Since

Before we differentiate, we can simplify a little more so our differentiation is easier. Through the logarithm rule which states that

#f(x)=e^(3xln(2))#

Now, we can differentiate the function through the chain rule. The chain rule in the case of an exponential

#d/dx(e^u)=e^u*u'#

Here,

Plugging this into the chain rule expression previously identified, we see that

#f'(x)=e^(3xln(2))*3ln(2)#

Careful! This is not fully simplified. Recall that

#f'(x)=2^(3x)(3ln(2))#

Note that what we just did can be generalized. This is a semi-useful "mold" to commit to memory, although you could do the work every time:

#d/dx(a^u)=a^u*ln(a)*u'#

Where