How do you differentiate $f (x) = 23^{x}$ $f(x)=23^x$ ?

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How do you differentiate $f (x) = 23^{x}$ $f(x)=23^x$ ?

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Answer 1 · 2017-03-08T18:43:19

$\frac{d}{d x} 23^{x} = 23^{x} ln 23$ $d/(dx) 23^x = 23^x ln 23$

Explanation:

Use:

$23 = e^{ln (23)}$ $23 = e^ln(23)$

${(a^{b})}^{c} = a^{b c}$ $(a^b)^c = a^(bc)" "$ when $a > 0$ $a > 0$

$\frac{d}{d x} e^{x} = e^{x}$ $d/(dx) e^x = e^x$

$d/(dx) u(v(x)) = u'(v(x))*v'(x)$

So:

$d/(dx) 23^x = d/(dx) (e^(ln 23))^x = d/(dx) e^((ln 23)x) = e^((ln 23) x) ln 23 = 23^x ln 23$

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How do you differentiate $f (x) = 23^{x}$ $f(x)=23^x$ ?

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