# What is the derivative of # ArcSin[x^(1/2)]#?

##### 1 Answer

Dec 4, 2016

#### 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 use the chain rule.

Let

Differentiate Implicitly:

# cosydy/dx = 1/2x^(-1/2) #

# :. cosydy/dx = 1/(2sqrt(x)) # ..... [1]

Using the

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

# :. cos^2y=1-sin^2y #

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

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

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

Substituting into [1]