How do you differentiate $f (x) = 2^{x}$ $f(x)=2^x$ ?

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Answer 1 · 2016-08-08T11:32:07

$f'(x) =2^xln(2)$

$f(x) = y = 2^x$

Take natural logs of both sides:

$ln(y) = ln(2^x) = xln(2)$

Implicitly differentiate both sides:

$1/y * (dy)/(dx) = ln(2)$

$(dy)/(dx) = yln(2)$

$y = 2^x implies (dy)/(dx) = 2^xln(2)$

How do you differentiate f(x)=2^xf(x)=2xf(x)=2^x?