How do you use the chain rule to differentiate #root11(lnx)#?

1 Answer
mason m
Sep 25, 2016

#1/(11x(lnx)^(10/11))#

Explanation:

This can be written as:

#y=(lnx)^(1/11)#

Which can be differentiated using the chain rule. The outside function is #x^(1/11)#, whose derivative is #1/11x^(-10/11)#. The derivative of the inside function, the inside function being #lnx#, is #1/x#.

So, the chain rule tells us that:

#dy/dx=1/11(lnx)^(-10/11)*1/x#

#dy/dx=1/(11x(lnx)^(10/11))#

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