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

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Answer 1 · 2018-04-05T11:10:28

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

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 $1/(e^(4x)+3x)*(4e^(4x)+3)$

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

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