Question

How do you find the derivative of `(arcsinx)^7`?

Answer 1

`(7(arcsinx)^6)/sqrt(1-x^2)`

Explanation:

We know from the power rule that the derivative of `x^7` is `7x^6`. The chain rule tells us that when we have a function inside this, the derivative will be in the same form of `7("function")^6` but multiplied by the derivative of the inner function as well.

So, the derivative of `(f(x))^7` is `7(f(x))^6*f'(x)`. So, for this, we see that the derivative of `(arcsinx)^7` is `7(arcsinx)^6*1/sqrt(1-x^2)`, since the derivative of `arcsinx` is `1/sqrt(1-x^2)`.