# What is the derivative of #cos^-1(x)#?

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Steve M
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Feb 7, 2017

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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.

Let

Differentiate Implicitly:

# -sinydy/dx = 1 # ..... [1]

Using the

# sin^2y+cos^2y -= 1 #

# :. sin^2y+x^2 = 1 #

# :. sin^2y = 1 -x^2#

# :. siny = sqrt(1 -x^2)#

Substituting into [1]

# :. -sqrt(1 -x^2)dy/dx=1 #

# :. dy/dx = -1/sqrt(1 -x^2) #

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