# How do you find the derivative of #arcsin(x^2/4)#?

##### 1 Answer

Nov 15, 2016

# d/dxarcsin(x^2/4) = (x)/(2sqrt(1-x^2/16)) #

#### Explanation:

# siny = x^2/4 # ..... [1]

We can now differentiate implicitly to get:

# cos(y)dy/dx = x/2 # ..... [2]

Using the fundamental trig identity

# sin^2(y)+cos^2(y)=1#

# :. (x^2/4)^2+cos^2(y)=1# (from [1])

# :. cos^2(y)=1-x^2/16#

# :. cos(y)=sqrt(1-x^2/16)#

Substituting into [2] we get:

# sqrt(1-x^2/16)dy/dx = x/2 #

# :. dy/dx = (x)/(2sqrt(1-x^2/16)) #