Question

If `f(x) =tan^2x` and `g(x) = sqrt(5x-1`, what is `f'(g(x))`?

Answer 1

`f'(g(x))=(5sec^2(sqrt(5x-1))tan(sqrt(5x-1)))/(sqrt(5x-1))`

Explanation:

To find `f'(g(x))`, we can start by finding `f(g(x))` and then take the derivative. We substitute `sqrt(5x-1)` into `f(x)`, so we have:

`f(g(x))=f(sqrt(5x-1))=tan^2(sqrt(5x-1))`

Now we take the derivative using the chain rule.

`2tan(sqrt(5x-1))*sec^2(sqrt(5x-1))*1/2(5x-1)^(-1/2)*5`

`=>(5sec^2(sqrt(5x-1))tan(sqrt(5x-1)))/(sqrt(5x-1))`