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

##### 1 Answer

Nov 15, 2016

# dy/dx = 5/sqrt(1-25x^2) #

#### Explanation:

# siny = 5x # ..... [1]

We can now differentiate implicitly to get:

# cos(y)dy/dx = 5 # ..... [2]

Using the fundamental trig identity

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

# :. (5x)^2+cos^2(y)=1# (from [1])

# :. cos^2(y)=1-25x^2#

# :. cos(y)=sqrt(1-25x^2)#

Substituting into [2] we get:

# sqrt(1-25x^2)dy/dx = 5 #

# :. dy/dx = 5/sqrt(1-25x^2) #