How do we differentiate #ln(e^(3x))#?

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Answer 1 · 2017-02-22T16:56:57

#3. d/dx(lne^(3x))= 3#

I'll answer number #3# for you,

Use properties of logarithms to simplify #lna^n = nlna#.

#lne^(3x) = 3xlne#

The function #y = lnx# and #y = e^x# are inverses. This means their product is #1#.

#=3x#

This, by the power rule, has derivative #3#.

Hopefully this helps!