Question

How do you find the derivative of the function `y = arc cos e^(4x)`?

Answer 1

`dy/dx=-(4e^(4x))/sqrt(1-e^(8x))`

Explanation:

The derivative of `arccos(x)` is `d/dx(arccos(x))=-1/sqrt(1-x^2)` and we also know `d/dx(e^(x))=e^(x)`. We can combine these facts, as well as the Chain Rule (`d/dx(f(g(x)))=f'(g(x))*g'(x)`) to say that, for `y=arccos(e^(4x))`, we get

`dy/dx=-1/sqrt(1-(e^(4x))^2)*d/dx(e^(4x))=-(4e^(4x))/sqrt(1-e^(8x))`