# How do you differentiate #y = tan^3(x^3)#?

##### 1 Answer

Jul 27, 2015

Use the chain rule twice.

#### Explanation:

It is important to remember the convention for powers of trigonometric functions:

**then** find the tangent of that number and **finally** raise that tangent to the third power". In notation:

The outermost function is the (second) cube.

And we know that

In this case

So we get

Now we need the derivative of

We'll use the chain rule again:

We get

#= sec^2(x^3)* 3x^2#

Putting it all together, we have:

Which can be written: