How do you find the derivative of $3^{x}$ $3^x$ ?

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Answer 1 · 2016-11-23T15:39:08

$\frac{d y}{d x} = 3^{x} ln 3$ $(dy)/(dx)=3^xln3$

using logarithmic differentiation

$y = 3^{x}$ $y=3^x$

take natural logs to both sides

$ln y = {ln 3}^{x} = x ln 3$ $lny=ln3^x=xln3$

differentiate $w r t x$ $wrt" " x$

$\frac{1}{y} \frac{d y}{d x} = ln 3$ $1/y(dy)/(dx)=ln3$

$\frac{d y}{d x} = y ln 3$ $(dy)/(dx)=yln3$

substitute back

$\frac{d y}{d x} = 3^{x} ln 3$ $(dy)/(dx)=3^xln3$

How do you find the derivative of 3^x3x3^x?