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

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

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

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

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

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

Simplify

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

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