What is the derivative of (x+7/(4x^2e^x)) ?

The derivative of (x+7/(4x^2e^x)) is -(x^2+8x+14)/(4e^xx^3)

What is the first derivative of (x+7/(4x^2e^x)) ?

The first derivative of (x+7/(4x^2e^x)) is -(x^2+8x+14)/(4e^xx^3)

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\frac{d}{d x} (\frac{x + 7}{4 x ^{2} e ^{x}})

- \frac{x ^{2} + 8 x + 14}{4 e ^{x} x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x + 7}{4 x ^{2} e ^{x}})

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{x + 7}{x ^{2} e ^{x}})

Apply the Quotient Rule:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( x + 7 ) x ^{2} e ^{x} - \frac{d}{d x} ( x ^{2} e ^{x} ) ( x + 7 )}{( x ^{2} e ^{x} ) ^{2}}

\frac{d}{d x} (x + 7) = 1

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

= \frac{1}{4} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x + 7 )}{( x ^{2} e ^{x} ) ^{2}}

Simplify

\frac{1}{4} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x + 7 )}{( x ^{2} e ^{x} ) ^{2}} : - \frac{x ^{2} + 8 x + 14}{4 e ^{x} x ^{3}}

= - \frac{x ^{2} + 8 x + 14}{4 e ^{x} x ^{3}}

\int arcsin (\frac{4}{3} x + 5) d x

(x^{3} + 2)^{5}, at x = - 1

\frac{\partial}{\partial x} (56 y^{4} x^{6} - 42 y^{3} x^{5})

(x - 1)^{2} (x - 2)^{3}

n = 1 \sum \infty 8 ((\frac{1}{5})^{n})

What is the derivative of (x+7/(4x^2e^x)) ?
The derivative of (x+7/(4x^2e^x)) is -(x^2+8x+14)/(4e^xx^3)
What is the first derivative of (x+7/(4x^2e^x)) ?
The first derivative of (x+7/(4x^2e^x)) is -(x^2+8x+14)/(4e^xx^3)