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

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

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

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

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derivative of

e^{\frac{z}{( z - 3 )}}

- \frac{3 e ^{\frac{z}{z - 3}}}{( z - 3 ) ^{2}}

Solution steps

\frac{d}{d z} (e^{\frac{z}{z - 3}})

Apply the chain rule:

e^{\frac{z}{z - 3}} \frac{d}{d z} (\frac{z}{z - 3})

= e^{\frac{z}{z - 3}} \frac{d}{d z} (\frac{z}{z - 3})

\frac{d}{d z} (\frac{z}{z - 3}) = - \frac{3}{( z - 3 ) ^{2}}

= e^{\frac{z}{z - 3}} (- \frac{3}{( z - 3 ) ^{2}})

Simplify

e^{\frac{z}{z - 3}} (- \frac{3}{( z - 3 ) ^{2}}) : - \frac{3 e ^{\frac{z}{z - 3}}}{( z - 3 ) ^{2}}

= - \frac{3 e ^{\frac{z}{z - 3}}}{( z - 3 ) ^{2}}

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