How do you find the derivative of the function: arccos(arcsin x)?

1 Answer
Jan 20, 2016

dy/dx = -1/sqrt(1-(arcsin(x))^2)**1/sqrt(1-x^2)

Explanation:

To find the derivative of arccos(arcsin(x))

The chain rule looks like a good choice here

Let y=arccos(arcsin(x))

Differentiating using color(magenta)"Chain Rule"

dy/dx = -1/sqrt(1-(arcsin(x))^2)**d/dx(arcsin(x))

dy/dx = -1/sqrt(1-(arcsin(x))^2)**1/sqrt(1-x^2) Answer