Question

How do you find the derivative of the function: `y = arcsin(x^5)`?

Answer 1

`dy/dx=(5x^4)/sqrt(1-x^10)`

Explanation:

Use the chain rule . To do this, you must first know that

`d/dxarcsin(x)=1/sqrt(1-x^2)`

Thus,

`d/dxarcsin(f(x))=1/sqrt(1-(f(x))^2)*f'(x)`

So, for `arcsin(x^5)` we see that `f(x)=x^5`, and

`dy/dx=d/dxarcsin(x^5)=1/sqrt(1-(x^5)^2)*d/dx(x^5)`

`dy/dx=(5x^4)/sqrt(1-x^10)`