# How do you find the derivative of # arcsin(x^2)#?

##### 1 Answer

Feb 21, 2017

#### Explanation:

When tackling the derivative of inverse trig functions. I prefer to rearrange and use Implicit differentiation as I always get the inverse derivatives muddled up, and this way I do not need to remember the inverse derivatives. If you can remember the inverse derivatives then you can use the chain rule.

Let

Differentiate Implicitly:

# cosydy/dx = 2x # ..... [1]

Using the

# sin^2y+cos^2y -= 1 #

# :. (x^2)^2+cos^2y=1 #

# :. cos^2y=1-x^4 #

# :. cosy=sqrt(1-x^4) #

Substituting into [1]