What is the derivative of f(z)=e^{z/((z-5))} ?

The derivative of f(z)=e^{z/((z-5))} is -(5e^{z/(z-5)})/((z-5)^2)

What is the first derivative of f(z)=e^{z/((z-5))} ?

The first derivative of f(z)=e^{z/((z-5))} is -(5e^{z/(z-5)})/((z-5)^2)

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derivative of

f (z) = e^{\frac{z}{( z - 5 )}}

- \frac{5 e ^{\frac{z}{z - 5}}}{( z - 5 ) ^{2}}

Solution steps

\frac{d}{d z} (e^{\frac{z}{z - 5}})

Apply the chain rule:

e^{\frac{z}{z - 5}} \frac{d}{d z} (\frac{z}{z - 5})

= e^{\frac{z}{z - 5}} \frac{d}{d z} (\frac{z}{z - 5})

\frac{d}{d z} (\frac{z}{z - 5}) = - \frac{5}{( z - 5 ) ^{2}}

= e^{\frac{z}{z - 5}} (- \frac{5}{( z - 5 ) ^{2}})

Simplify

e^{\frac{z}{z - 5}} (- \frac{5}{( z - 5 ) ^{2}}) : - \frac{5 e ^{\frac{z}{z - 5}}}{( z - 5 ) ^{2}}

= - \frac{5 e ^{\frac{z}{z - 5}}}{( z - 5 ) ^{2}}

What is the derivative of f(z)=e^{z/((z-5))} ?
The derivative of f(z)=e^{z/((z-5))} is -(5e^{z/(z-5)})/((z-5)^2)
What is the first derivative of f(z)=e^{z/((z-5))} ?
The first derivative of f(z)=e^{z/((z-5))} is -(5e^{z/(z-5)})/((z-5)^2)