How do you use the chain rule to differentiate #lnx^100#?

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Answer 1 · 2017-02-08T02:22:29

#dy/dx = 100/x#

Method 1: Using the chain rule

Let #y = ln u# and #u = x^100#. Then #dy/(du) = 1/u# and #(du)/dx = 100x^99#.

#dy/dx = dy/(du) * (du)/dx#

#dy/dx = 1/u * 100x^99#

#dy/dx = 1/x^100 * 100x^99#

#dy/dx = 100/x#

Method 2: Using logarithm laws

Apply the rule #loga^n = nloga# to simplify prior to differentiating.

#y = 100lnx#

#dy/dx = 100/x -> "since" d/dx lnx = 1/x#