What is the difference between the chain rule and the power rule? Are they simply different forms of each other?

1 Answer
Steve M
Nov 11, 2016

They are very different !

The "power rule" is used to differentiate a fixed power of #x# e.g. #x^3#

The "chain rule" is used to differentiate a function of a function, e.g. #e^cosx#, #sin(x^3)#, #(1+lnx)^5# etc

Explanation:

Power Rule
# d/dx(x^n)=nx^n-1 # where #n' is a constant

Chain Rule

# d/dx(f(g(x) ) = f'(g(x)) * g'(x) # or # dy/dx=dy/(du)*(du)/dx #

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