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

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

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

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

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\frac{d}{d x} (e^{\frac{3 x}{2}})

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

Solution steps

\frac{d}{d x} (e^{\frac{3 x}{2}})

Apply the chain rule:

e^{\frac{3 x}{2}} \frac{d}{d x} (\frac{3 x}{2})

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

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

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

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\frac{64}{x ^{2} + 16}, at x = 3

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