How do I find $f'(x)$ for $f(x)=5^x$ ?

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How do I find $f'(x)$ for $f(x)=5^x$ ?

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Answer 1 · 2018-04-04T06:18:09

$dy/dx = 5^x log5$

Explanation:

$y=5^x$

$logy=x log5$

$dy/dx. 1/y=x.(0)+log5.(1)$

$dy/dx . 1/y =log5$

$dy/dx =log5 . y$

$dy/dx =log5 . 5^x$

$dy/dx = 5^x log5$

Answer 2 · 2018-04-04T06:21:23

$f(x)=y=5^x$

Taking log on both the sides,

$logy=log5^x$

$logy=xlog5$ $color(white)(wwggggggggggggw$ $["as " color(red)(loga^b = bloga)]$

Now, applying implicit differentiation,
$1/y dy/dx=x (d(log5))/dx + log5$ $color(white)(o$ $["product rule is applied on "xlog5 ]$

$dy/dx=y[x + log5]$ $color(white)(gggggggw$ $["as derivative of a constant is 1" ]$

$dy/dx=5^x[x + log5]$

Answer 3 · 2018-04-04T06:27:56

$f'(x)=ln5*5^x$

Explanation:

Let $y=f(x)=5^x$

then $lny=xln5$ and differentiating we get

$1/y(dy)/(dx)=ln5$

or $(dy)/(dx)=ln5*y=ln5*5^x$

Answer 4 · 2018-04-04T14:00:20

$5^x*ln5$

Explanation:

Given: $f(x)=5^x$

Using the common integral that $(a^x)'=a^xlna$ , we get:

$f'(x)=5^x*ln5$

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How do I find $f'(x)$ for $f(x)=5^x$ ?

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