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)) #