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

Oct 3, 2016

Deivative of $\arcsin \left(5 x + 5\right)$ is $\frac{5}{\sqrt{1 - 25 {\left(x + 1\right)}^{2}}}$

#### Explanation:

Let us first find the derivative of $\arcsin x$ and let $y = \arcsin x$,

Then $x = \sin y$ and $\frac{\mathrm{dx}}{\mathrm{dy}} = \cos y = \sqrt{1 - {\sin}^{2} y} = \sqrt{1 - {x}^{2}}$

or $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{\sqrt{1 - {x}^{2}}}$ i.e. derivative of $\arcsin x$ is $\frac{1}{\sqrt{1 - {x}^{2}}}$

Now using chain rule deivative of $\arcsin \left(5 x + 5\right)$ is

$\frac{1}{\sqrt{1 - {\left(5 x + 5\right)}^{2}}} \times 5 = \frac{5}{\sqrt{1 - 25 {\left(x + 1\right)}^{2}}}$