What is the derivative of ((x-8))/(9x^2e^x) ?

The derivative of ((x-8))/(9x^2e^x) is (-x^2+7x+16)/(9e^xx^3)

What is the first derivative of ((x-8))/(9x^2e^x) ?

The first derivative of ((x-8))/(9x^2e^x) is (-x^2+7x+16)/(9e^xx^3)

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derivative of

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

\frac{- x ^{2} + 7 x + 16}{9 e ^{x} x ^{3}}

Solution steps

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

Take the constant out:

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

= \frac{1}{9} \frac{d}{d x} (\frac{x - 8}{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 - 8 ) x ^{2} e ^{x} - \frac{d}{d x} ( x ^{2} e ^{x} ) ( x - 8 )}{( x ^{2} e ^{x} ) ^{2}}

\frac{d}{d x} (x - 8) = 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 - 8 )}{( 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 - 8 )}{( x ^{2} e ^{x} ) ^{2}} : \frac{- x ^{2} + 7 x + 16}{9 e ^{x} x ^{3}}

= \frac{- x ^{2} + 7 x + 16}{9 e ^{x} x ^{3}}

x^{^{'}} = (1 - x) \cdot 0.03 - \frac{( 0.03 x )}{( e ^{3} - 1 )}

y^{^{'}} - \frac{2 y}{x} = - x^{2} y^{2}

\int \frac{a x}{x ^{4} + b ^{4}} d x

x \to 0 lim (\frac{- 1}{5 x})

f (x) = sec^{2} (2 x)

What is the derivative of ((x-8))/(9x^2e^x) ?
The derivative of ((x-8))/(9x^2e^x) is (-x^2+7x+16)/(9e^xx^3)
What is the first derivative of ((x-8))/(9x^2e^x) ?
The first derivative of ((x-8))/(9x^2e^x) is (-x^2+7x+16)/(9e^xx^3)