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

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

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

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

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

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

Solution steps

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

Simplify

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

= \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}

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