How do we differentiate $ln (e^{3 x})$ $ln(e^(3x))$ ?

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Answer 1 · 2017-02-22T16:56:57

$3 . \frac{d}{d x} ({ln e}^{3 x}) = 3$ $3. d/dx(lne^(3x))= 3$

I'll answer number $3$ $3$ for you,

Use properties of logarithms to simplify ${ln a}^{n} = n ln a$ $lna^n = nlna$ .

${ln e}^{3 x} = 3 x ln e$ $lne^(3x) = 3xlne$

The function $y = ln x$ $y = lnx$ and $y = e^{x}$ $y = e^x$ are inverses. This means their product is $1$ $1$ .

$= 3 x$ $=3x$

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

Hopefully this helps!

How do we differentiate ln(e^(3x))ln(e3x)ln(e^(3x))?