How do you differentiate #y = tan^3(x^3)#?
Use the chain rule twice.
It is important to remember the convention for powers of trigonometric functions:
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:
#= sec^2(x^3)* 3x^2#
Putting it all together, we have:
Which can be written: