What is the derivative of e^{z/(z-6)} ?

The derivative of e^{z/(z-6)} is -(6e^{z/(z-6)})/((z-6)^2)

What is the first derivative of e^{z/(z-6)} ?

The first derivative of e^{z/(z-6)} is -(6e^{z/(z-6)})/((z-6)^2)

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derivative of

e^{\frac{z}{z - 6}}

- \frac{6 e ^{\frac{z}{z - 6}}}{( z - 6 ) ^{2}}

Solution steps

\frac{d}{d z} (e^{\frac{z}{z - 6}})

Apply the chain rule:

e^{\frac{z}{z - 6}} \frac{d}{d z} (\frac{z}{z - 6})

= e^{\frac{z}{z - 6}} \frac{d}{d z} (\frac{z}{z - 6})

\frac{d}{d z} (\frac{z}{z - 6}) = - \frac{6}{( z - 6 ) ^{2}}

= e^{\frac{z}{z - 6}} (- \frac{6}{( z - 6 ) ^{2}})

Simplify

e^{\frac{z}{z - 6}} (- \frac{6}{( z - 6 ) ^{2}}) : - \frac{6 e ^{\frac{z}{z - 6}}}{( z - 6 ) ^{2}}

= - \frac{6 e ^{\frac{z}{z - 6}}}{( z - 6 ) ^{2}}

\int \frac{16 s - 4}{3 - 2 s + 4 s ^{2}} d s

y = tan (e^{3 t}) + e^{t a n (3 t)}

f (x) = e^{r} + r^{e}

\int \frac{3 x}{x ^{2}} d x

f^{^{'}} (x) = 3 sec (x)

What is the derivative of e^{z/(z-6)} ?
The derivative of e^{z/(z-6)} is -(6e^{z/(z-6)})/((z-6)^2)
What is the first derivative of e^{z/(z-6)} ?
The first derivative of e^{z/(z-6)} is -(6e^{z/(z-6)})/((z-6)^2)