Question

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

Answer 1

`Sec^2(arcsin x)/sqrt(1-x^2)`

or `Sec^2(sin^-1 x)/sqrt(1-x^2)`

Explanation:

to find the derivative of the function `tan(arcsin x)`, use the following formulas for differentiation

`d/dx(tan u) = sec^2 u * d/dx(u)` and

`d/dx(arcsin u)= 1/sqrt(1-u^2)*d/dx(u)`

let me continue

from the given `tan(arcsin x)`

`d/dx(tan(arcsin x))=sec^2 (arcsin x)*d/dx(arcsin x)`

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

the final answer is

`= sec^2 (arcsin x)/sqrt(1-x^2)`