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) #