What is the derivative of 4e^{sqrt(x)} ?

The derivative of 4e^{sqrt(x)} is (2e^{sqrt(x)})/(sqrt(x))

What is the first derivative of 4e^{sqrt(x)} ?

The first derivative of 4e^{sqrt(x)} is (2e^{sqrt(x)})/(sqrt(x))

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\frac{d}{d x} (4 e^{x})

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

Solution steps

\frac{d}{d x} (4 e^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (e^{x})

Apply the chain rule:

e^{x} \frac{d}{d x} (x)

= e^{x} \frac{d}{d x} (x)

\frac{d}{d x} (x) = \frac{1}{2 x}

= 4 e^{x} \frac{1}{2 x}

Simplify

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

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

\int 2 e^{3} d x

\frac{d}{d x} (a \cdot sinh (\frac{x}{a}))

\int \frac{1}{4 x ^{2} + 16} d x

\frac{d}{d t} (t cos (2 t))

4 x + \frac{1}{x}

What is the derivative of 4e^{sqrt(x)} ?
The derivative of 4e^{sqrt(x)} is (2e^{sqrt(x)})/(sqrt(x))
What is the first derivative of 4e^{sqrt(x)} ?
The first derivative of 4e^{sqrt(x)} is (2e^{sqrt(x)})/(sqrt(x))