Question

Find the derivative of:
tan(x^2+x)^5

Answer 1

You need to apply the chain rule for this.
First take the derivative of the outside function multiplied by the derivative of the inner function.
So, here you have: \(\sf \color{blue}{[tan(x^2+x)]^5} \) which is almost the same thing as thinking: \(\sf \color{red}{a^5}\),
where a = tan(x\(^2\)+x)

So you have the first derivative of the outer function is: \(\sf \color{green}{5[tan(x^2+x)]^4} \times\frac{d}{dx}tan(x^2+x)\)
where you can see it as: \(\sf \frac{d}{dx}\color{orange}{tan(b)}\)
where b = x\(^2\)+x

then do the same thing with the LAST inner function, and multiply by that again.

Answer 2

thank you very much... I see where I made my error...