How do you find the derivative of #y=arcsin(x^4)#?
1 Answer
Dec 13, 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 can use the chain rule.
Differentiate Implicitly:
# cosydy/dx = 4x^3 # ..... [1]
Using the
# sin^2y+cos^2y -= csc^2y #
# :. (x^4)^2+cos^2y=1 #
# :. cos^2y=1-x^8 #
# :. cosy=sqrt(1-x^8) #
Substituting into [1]
