# How do you find the derivative of #sin^-1(2x+1)#?

##### 2 Answers

The answer is

#### Explanation:

For this equation you would use the **[chain rule]** (https://socratic.org/calculus/basic-differentiation-rules/chain-rule) so you take the **derivative of the outside**:

**times the derivative of the inside**:

So the derivative of ** #sin^-1# otherwise known as #arcsin#** is

Differentiating Inverse Trigonometric Functions

but in this case

Next the derivative of

So the answer becomes **outside times inside**

Which is

Here are the derivatives of **inverse functions**

#### Explanation:

Given:

Note that

So

Note that

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Set

Note that

Set the value of the Hypotenuse to 1 giving:

Using

But

as the hypotenuse is 1 we have

So equation(1) becomes:

But by Pythagoras

Thus