How do I find the derivative of the function #y = sin(tan(4x))#?
You have a composite function, which are to be derived using the chain formula. If you're in the case
In these cases, you simply need to derive the most "external" function, and then multply the result by the derivative of the internal one, and so on.
First of all, let's remark the derivatives of your three functions: you have that
You would need to use the chain rule to find this derivative, because you are dealing with composite functions. Composite functions are functions where one (or more) functions are composed in another function. You can think of it as having an "outer" function with an "inner" function composed in it.
Here, finding the inner and outer functions is quite straight forward. In
In words, the chain rule says:
The derivative of the outer function (with the inner function left alone) times the derivative of the inner function
In this case, we expand it to derive the second composite function (after deriving its outer function left alone).
First we need to derive the
NOTE 1: This isn't the completed derivation problem, I'm just showing a combination of steps that I will combine in the end- So I'm leaving deriving the inner functions in seperate steps.
Okay, now we need to derive the first inner function, that is
Finally, we derive the last inner function.
NOTE 2: This is where we do the actual correct derivation, by combining the steps