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Popular >

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

Solution

derivative of

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

Solution

- \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}}

Popular Examples

(d^2y)/(dx^2)=sqrt(2x-3)

\frac{d ^{2} y}{d x ^{2}} = 2 x - 3

limit as x approaches 2-of (x+2)/(x^2-4)

x \to 2 - lim (\frac{x + 2}{x ^{2} - 4})

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\int_{0}^{1} \frac{4}{1 + x ^{2}} d x

derivative of e^{xy}y

\frac{d}{d x} (e^{x y} y)

Frequently Asked Questions (FAQ)

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)