How do you differentiate $ln(x+4+e^-3x)$ ?

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Answer 1 · 2018-03-14T13:24:45

$color(blue)((1-3e^(-3x))/(x+4+e^(-3x)))$

If:

$y=ln(x)<=>e^y=x$

Using this definition for the given function:

$e^y=x+4+e^(-3x)$

Differentiating implicitly:

$e^ydy/dx=1+0-3e^(-3x)$

Dividing by: $color(white)(88)bb(e^y)$

$dy/dx=(1-3e^(-3x))/e^y$

From above:

$e^y=x+4+e^(-3x)$

$:.$

$dy/dx=color(blue)((1-3e^(-3x))/(x+4+e^(-3x)))$

How do you differentiate ln(x+4+e^-3x) ln(x+4+e^-3x)?