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Popular >

derivative of f(x)=e^{x/((x-9))}

Solution

derivative of

f (x) = e^{\frac{x}{( x - 9 )}}

Solution

- \frac{9 e ^{\frac{x}{x - 9}}}{( x - 9 ) ^{2}}

Solution steps

\frac{d}{d x} (e^{\frac{x}{x - 9}})

Apply the chain rule:

e^{\frac{x}{x - 9}} \frac{d}{d x} (\frac{x}{x - 9})

= e^{\frac{x}{x - 9}} \frac{d}{d x} (\frac{x}{x - 9})

\frac{d}{d x} (\frac{x}{x - 9}) = - \frac{9}{( x - 9 ) ^{2}}

= e^{\frac{x}{x - 9}} (- \frac{9}{( x - 9 ) ^{2}})

Simplify

e^{\frac{x}{x - 9}} (- \frac{9}{( x - 9 ) ^{2}}) : - \frac{9 e ^{\frac{x}{x - 9}}}{( x - 9 ) ^{2}}

= - \frac{9 e ^{\frac{x}{x - 9}}}{( x - 9 ) ^{2}}

Popular Examples

d/(ds)((2s^2)/((s-6)^3))

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1/t (dy)/(dt)-1/(1+t^2)=0,y(0)=1

\frac{1}{t} \frac{d y}{d t} - \frac{1}{1 + t ^{2}} = 0, y (0) = 1

limit as t approaches 0 of 1/2 e^{-2t}

t \to 0 lim (\frac{1}{2} e^{- 2 t})

(\partial)/(\partial x)(4x+6y)

\frac{\partial}{\partial x} (4 x + 6 y)

integral of e^{-(x+y)}

\int e^{- (x + y)} d y

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=e^{x/((x-9))} ?
The derivative of f(x)=e^{x/((x-9))} is -(9e^{x/(x-9)})/((x-9)^2)
What is the first derivative of f(x)=e^{x/((x-9))} ?
The first derivative of f(x)=e^{x/((x-9))} is -(9e^{x/(x-9)})/((x-9)^2)