What is the derivative of (x+3/(8x^2e^x)) ?

The derivative of (x+3/(8x^2e^x)) is -(x^2+4x+6)/(8e^xx^3)

What is the first derivative of (x+3/(8x^2e^x)) ?

The first derivative of (x+3/(8x^2e^x)) is -(x^2+4x+6)/(8e^xx^3)

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\frac{d}{d x} (\frac{x + 3}{8 x ^{2} e ^{x}})

- \frac{x ^{2} + 4 x + 6}{8 e ^{x} x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x + 3}{8 x ^{2} e ^{x}})

Take the constant out:

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

= \frac{1}{8} \frac{d}{d x} (\frac{x + 3}{x ^{2} e ^{x}})

Apply the Quotient Rule:

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

= \frac{1}{8} \cdot \frac{\frac{d}{d x} ( x + 3 ) x ^{2} e ^{x} - \frac{d}{d x} ( x ^{2} e ^{x} ) ( x + 3 )}{( x ^{2} e ^{x} ) ^{2}}

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

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

= \frac{1}{8} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x + 3 )}{( x ^{2} e ^{x} ) ^{2}}

Simplify

\frac{1}{8} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x + 3 )}{( x ^{2} e ^{x} ) ^{2}} : - \frac{x ^{2} + 4 x + 6}{8 e ^{x} x ^{3}}

= - \frac{x ^{2} + 4 x + 6}{8 e ^{x} x ^{3}}

x \to 0 + lim (2^{x})

\int \frac{e ^{x}}{e ^{2 x} + e ^{x} + 2} d x

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

x \to 0 + lim (x^{6 s i n (x)})

\int_{0}^{\frac{π}{2}} \frac{cos ( t )}{1 + sin ^{2} ( t )} d t

What is the derivative of (x+3/(8x^2e^x)) ?
The derivative of (x+3/(8x^2e^x)) is -(x^2+4x+6)/(8e^xx^3)
What is the first derivative of (x+3/(8x^2e^x)) ?
The first derivative of (x+3/(8x^2e^x)) is -(x^2+4x+6)/(8e^xx^3)