What is the derivative of (x-5)/(9x^2e^x) ?

The derivative of (x-5)/(9x^2e^x) is (-x^2+4x+10)/(9e^xx^3)

What is the first derivative of (x-5)/(9x^2e^x) ?

The first derivative of (x-5)/(9x^2e^x) is (-x^2+4x+10)/(9e^xx^3)

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derivative of

\frac{x - 5}{9 x ^{2} e ^{x}}

\frac{- x ^{2} + 4 x + 10}{9 e ^{x} x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x - 5}{9 x ^{2} e ^{x}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{9} \frac{d}{d x} (\frac{x - 5}{x ^{2} e ^{x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{9} \cdot \frac{\frac{d}{d x} ( x - 5 ) x ^{2} e ^{x} - \frac{d}{d x} ( x ^{2} e ^{x} ) ( x - 5 )}{( x ^{2} e ^{x} ) ^{2}}

\frac{d}{d x} (x - 5) = 1

\frac{d}{d x} (x^{2} e^{x}) = 2 x e^{x} + e^{x} x^{2}

= \frac{1}{9} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x - 5 )}{( x ^{2} e ^{x} ) ^{2}}

Simplify

\frac{1}{9} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x - 5 )}{( x ^{2} e ^{x} ) ^{2}} : \frac{- x ^{2} + 4 x + 10}{9 e ^{x} x ^{3}}

= \frac{- x ^{2} + 4 x + 10}{9 e ^{x} x ^{3}}

\frac{\partial}{\partial x} (2 x + y)

y^{^{'''}} + 3 y^{^{''}} + y^{^{'}} - 5 y = 0

\int 7 x^{6} d x

10 x e^{x}

\frac{d}{d x} (\frac{1}{18} (e^{9 x} + e^{- 9 x}))

What is the derivative of (x-5)/(9x^2e^x) ?
The derivative of (x-5)/(9x^2e^x) is (-x^2+4x+10)/(9e^xx^3)
What is the first derivative of (x-5)/(9x^2e^x) ?
The first derivative of (x-5)/(9x^2e^x) is (-x^2+4x+10)/(9e^xx^3)