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

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

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

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

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derivative of

e^{\frac{z}{z - 2}}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = 4 x^{2} + 7, (- 3, 43)

81 y^{^{''}} - 16 y = 0

x \to 7 lim (0)

\int_{0}^{5} x^{2} - 5 x d x

(1 + x) y^{^{'}} + 2 y = \frac{sin ( x )}{1 + x}

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