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What is the derivative of #cos^3(x)#?

1 Answer
Dec 18, 2014

The derivative of #cos^3(x)# is equal to:
#-3cos^2(x)*sin(x)#
You can get this result using the Chain Rule which is a formula for computing the derivative of the composition of two or more functions in the form: #f(g(x))#.
You can see that the function #g(x)# is nested inside the #f( )# function.
Deriving you get:
derivative of #f(g(x))# --> #f'(g(x))*g'(x)#

In this case the #f( )# function is the cube or #( )^3# while the second function "nested" into the cube is #cos(x)#.

First you deal with the cube deriving it but letting the argument #g(x)# (i.e. the #cos#) untouched and then you multiply by the derivative of the nested function.
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Which is equal to: #-3cos^2(x)*sin(x)#