What is the derivative of # ln(e^(4x)+3x)#?

1 Answer
Anish M. · David B.
Apr 5, 2018

#d/(dx) ln(e^(4x)+3x)=(4e^(4x)+3)/(e^(4x)+3x)#

Explanation:

Derivative of #lnx# is #1/x#

So derivative of #ln(e^(4x)+3x)# is #1/(e^(4x)+3x)d/dx(e^(4x)+3x)# (Chain rule)

Derivative of #e^(4x)+3x# is #4e^(4x)+3#

So derivative of #ln(e^(4x)+3x)# is #1/(e^(4x)+3x)*(4e^(4x)+3)#

#=(4e^(4x)+3)/(e^(4x)+3x)#

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