Question

How do you find the derivative of `arccose^x`?

Answer 1

`-e^x/(sqrt(1-e^(2x)))`

Explanation:

Use the `color(blue)"standard derivative result"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(arccosx)=-1/(sqrt(1-x^2)))color(white)(2/2)|)))`

differentiate using the `color(blue)("chain rule"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(arccos(f(x)))=-1/(sqrt(1-(f(x))^2)).f'(x))color(white)(2/2)|)))`

`rArrd/dx(arccose^x)`

`=-1/(sqrt(1-(e^x)^2))xxd/dx(e^x)`

`=-e^x/(sqrt(1-e^(2x))`