Question

Question #25a9e

Answer 1

The answer is:

`dy/dx = sqrt(5)/(sqrt(x)(2 + 10x))`

Here's how to do it.

`y= arctan(sqrt(5x))`

Because the equation is in the form of `f(g(x))`, we should use the chain rule.

`f(x) = arctan(g(x))`
`g(x) = sqrt(5x)`

The chain rule:
`dy/dx = f'(g(x))g'(x)`

Our case:
`f'(g(x)) = 1/(1+(sqrt(5x))^2) = 1/(1 + 5x)`
`g'(x) = (sqrt(5)/2) (x)^(-1/2)`

Plugging these values back into the chain rule gives us the following answer:

`dy/dx = sqrt(5)/(sqrt(x)(2 + 10x))`