What is the (sqrt(e^x))^' ?

The (sqrt(e^x))^' is (e^x)/(2sqrt(e^x))

What is the first (sqrt(e^x))^' ?

The first (sqrt(e^x))^' is (e^x)/(2sqrt(e^x))

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(e^{x})^{^{'}}

\frac{e ^{x}}{2 e ^{x}}

Solution steps

(e^{x})^{'}

Apply the chain rule:

\frac{1}{2 e ^{x}} (e^{x})^{'}

= \frac{1}{2 e ^{x}} (e^{x})^{'}

(e^{x})^{'} = e^{x}

= \frac{1}{2 e ^{x}} e^{x}

Simplify

\frac{1}{2 e ^{x}} e^{x} : \frac{e ^{x}}{2 e ^{x}}

= \frac{e ^{x}}{2 e ^{x}}

\int \frac{9}{x ( x ^{4} + 7 )} d x

\int 2 x^{2} cos (x^{3}) d x

f (x) = \frac{1}{x ^{3} + 2 x + 1}

ln (x^{3} + 3 x^{2} + 5 x + 6)

\frac{d}{d x} (2 x y - 1)