How do you find the derivative of $y = {(ln 2)}^{x}$ $y = (ln 2)^x$ ?

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Answer 1 · 2016-01-19T19:21:18

First, take the natural log of both sides of the equation. Then, use implicit differentiation ...

$y = {(ln 2)}^{x}$ $y = (ln 2)^x$

$ln y = ln [{(ln 2)}^{x}]$ $lny = ln[(ln 2)^x]$

Use the property of logs ...

$ln y = x {ln (ln 2)}$ $lny = xln(ln 2)^$

Now, implicit differentiation ...

$(1/y)y'=ln(ln2)$

Finally, solve for $y'$

$y'=yln(ln2)$

$=(ln2)^xln(ln2)$

hope that helped

How do you find the derivative of y = (ln 2)^xy=(ln2)xy = (ln 2)^x?