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

The derivative of (x+5/(2x^2e^x)) is -(x^2+6x+10)/(2e^xx^3)

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

The first derivative of (x+5/(2x^2e^x)) is -(x^2+6x+10)/(2e^xx^3)

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

- \frac{x ^{2} + 6 x + 10}{2 e ^{x} x ^{3}}

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \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}{2} \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}{2} \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}{2} \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} + 6 x + 10}{2 e ^{x} x ^{3}}

= - \frac{x ^{2} + 6 x + 10}{2 e ^{x} x ^{3}}

\int 1 - 36 x^{2} d x

f (x) = x + 24, (1, 5)

\frac{\partial}{\partial y} (3 x^{2} + 3 y^{2})

\frac{\partial}{\partial y} (\frac{3}{x ^{2} + y ^{2}})

\frac{d}{d x} (3 x^{3} (x^{2} + 4)^{4})

What is the derivative of (x+5/(2x^2e^x)) ?
The derivative of (x+5/(2x^2e^x)) is -(x^2+6x+10)/(2e^xx^3)
What is the first derivative of (x+5/(2x^2e^x)) ?
The first derivative of (x+5/(2x^2e^x)) is -(x^2+6x+10)/(2e^xx^3)