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

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

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

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

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derivative of

f (x) = \frac{x + 2}{7 x ^{2} e ^{x}}

- \frac{x ^{2} + 3 x + 4}{7 e ^{x} x ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 2) = 1

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

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

Simplify

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

= - \frac{x ^{2} + 3 x + 4}{7 e ^{x} x ^{3}}

\int_{0}^{t} e^{x} sin (t - x) d x

x \to 0 + lim (ln (2 x))

\frac{d y}{d t} + y = 5 sin (2 t)

\frac{d}{d x} (- 3 x + 1)

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

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