What is the derivative of # ArcSin[x^(1/2)]#?
1 Answer
Dec 4, 2016
Explanation:
When tackling the derivative of inverse trig functions. I prefer to rearrange and use Implicit differentiation as I always get the inverse derivatives muddled up, and this way I do not need to remember the inverse derivatives. If you can remember the inverse derivatives then you use the chain rule.
Let
Differentiate Implicitly:
# cosydy/dx = 1/2x^(-1/2) #
# :. cosydy/dx = 1/(2sqrt(x)) # ..... [1]
Using the
# sin^2y+cos^2y -=1#
# :. cos^2y=1-sin^2y #
# :. cos^2y=1-(sqrt(x))^2 #
# :. cos^2y=1-x #
# :. cosy=sqrt(1-x) #
Substituting into [1]
