What is the derivative of this function #sin^-1(x/4)#?
1 Answer
Nov 28, 2016
Explanation:
Let
Differentiate Implicitly:
# cosydy/dx = 1/4 # .... [1]
Using the fundamental Trig Identity
# sin^2y+cos^2y=1#
# :. (x/4)^2+cos^2y=1#
# :. x^2/16+cos^2y=1#
# :. cos^2y=1-x^2/16#
# :. cosy=sqrt(1-x^2/16) #
Substituting into [1]:
# sqrt(1-x^2/16)dy/dx = 1/4 #
# :. dy/dx = 1/(4sqrt(1-x^2/16)) #