What is the derivative of e^{x/(x-8}) ?

The derivative of e^{x/(x-8}) is -(8e^{x/(x-8)})/((x-8)^2)

What is the first derivative of e^{x/(x-8}) ?

The first derivative of e^{x/(x-8}) is -(8e^{x/(x-8)})/((x-8)^2)

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\frac{d}{d x} (e^{\frac{x}{x - 8}})

- \frac{8 e ^{\frac{x}{x - 8}}}{( x - 8 ) ^{2}}

Solution steps

\frac{d}{d x} (e^{\frac{x}{x - 8}})

Apply the chain rule:

e^{\frac{x}{x - 8}} \frac{d}{d x} (\frac{x}{x - 8})

= e^{\frac{x}{x - 8}} \frac{d}{d x} (\frac{x}{x - 8})

\frac{d}{d x} (\frac{x}{x - 8}) = - \frac{8}{( x - 8 ) ^{2}}

= e^{\frac{x}{x - 8}} (- \frac{8}{( x - 8 ) ^{2}})

Simplify

e^{\frac{x}{x - 8}} (- \frac{8}{( x - 8 ) ^{2}}) : - \frac{8 e ^{\frac{x}{x - 8}}}{( x - 8 ) ^{2}}

= - \frac{8 e ^{\frac{x}{x - 8}}}{( x - 8 ) ^{2}}

\int (9 x^{2} - 8 x) e^{2 x} d x

y^{^{''}} - 6 y + 9 y = 0

\frac{d y}{d x} = \frac{( 2 x ^{2} + 3 ) ( 3 x + 2 )}{7 x - 3}

(x + 1) \frac{d y}{d x} = x + 6

\frac{d}{d x} (co tan (2 x))

What is the derivative of e^{x/(x-8}) ?
The derivative of e^{x/(x-8}) is -(8e^{x/(x-8)})/((x-8)^2)
What is the first derivative of e^{x/(x-8}) ?
The first derivative of e^{x/(x-8}) is -(8e^{x/(x-8)})/((x-8)^2)