Question #25a9e

Question

1348 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-03-11T16:13:44

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:

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