Question

d/dx (cos(e^(tan3x)^1/2))

Answer 1

\[d/dx (\cos(e^\sqrt{\tan3x}))\]

Answer 2

You remember that the derivative of a composite function is the product of the derivative, ie d/dx [f(g(x)] = f'(g(x))*g'(x) and so on.
My personal opinion is: better leave the ^1/2 instead of the root, because the "n*x^(n-1) " works even if n is rational.
You have 5 "layers" of functions, and my tip is starting from the inside out and starting your derivative from it. Expect a "monster" product, just try to keep it readable when doing a test.

Answer 3

Alternatively, you can place "whatever is inside the cosine as t, and your derivative gets
\[{d \over dx } \cos [....] = {d \over dx } \cos t = -\sin t *{d \over dx } t\], rinse and repeat.

Answer 4

Thank you! I figured it out! :)