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

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

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

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

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

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

Solution steps

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

Simplify

e^{3 x} : e^{3 x}

= \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}

x \to 1 lim (3 1 - x)

\frac{( 12 x - 7 )}{3 x - 9}

f (x) = ln (3 x + 5)

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

\frac{d}{d x} (- \frac{1}{( x + 3 ) ^{2}})

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