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

Mar 7, 2018

$y ' = \frac{5}{1 - 25 {x}^{2}}$

#### Explanation:

Just a simple application of the chain rule which states that
$\frac{d}{\mathrm{dx}} f \left(g \left(x\right)\right) = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$

where $f \left(x\right) = \arcsin \left(x\right)$
and $g \left(x\right) = 5 x$

recall that the derivative of $\arcsin \left(x\right)$ is $\frac{1}{1 - {x}^{2}}$ and of $5 x$ is $5$

therefore,

the entire derivative is
$\frac{1}{1 - {\left(5 x\right)}^{2}} \cdot 5$
=
which is equal to