What is the derivative of e^{3sqrt(x)} ?

The derivative of e^{3sqrt(x)} is (3e^{3sqrt(x)})/(2sqrt(x))

What is the first derivative of e^{3sqrt(x)} ?

The first derivative of e^{3sqrt(x)} is (3e^{3sqrt(x)})/(2sqrt(x))

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derivative of

e^{3 x}

\frac{3 e ^{3 x}}{2 x}

Solution steps

\frac{d}{d x} (e^{3 x})

Apply the chain rule:

e^{3 x} \frac{d}{d x} (3 x)

= e^{3 x} \frac{d}{d x} (3 x)

\frac{d}{d x} (3 x) = \frac{3}{2 x}

= e^{3 x} \frac{3}{2 x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 e ^{3 x}}{2 x}

What is the derivative of e^{3sqrt(x)} ?
The derivative of e^{3sqrt(x)} is (3e^{3sqrt(x)})/(2sqrt(x))
What is the first derivative of e^{3sqrt(x)} ?
The first derivative of e^{3sqrt(x)} is (3e^{3sqrt(x)})/(2sqrt(x))