What is the derivative of (x-6/(7x^2e^x)) ?

The derivative of (x-6/(7x^2e^x)) is (-x^2+5x+12)/(7e^xx^3)

What is the first derivative of (x-6/(7x^2e^x)) ?

The first derivative of (x-6/(7x^2e^x)) is (-x^2+5x+12)/(7e^xx^3)

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\frac{d}{d x} (\frac{x - 6}{7 x ^{2} e ^{x}})

\frac{- x ^{2} + 5 x + 12}{7 e ^{x} x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x - 6}{7 x ^{2} e ^{x}})

Take the constant out:

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

= \frac{1}{7} \frac{d}{d x} (\frac{x - 6}{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 - 6 ) x ^{2} e ^{x} - \frac{d}{d x} ( x ^{2} e ^{x} ) ( x - 6 )}{( x ^{2} e ^{x} ) ^{2}}

\frac{d}{d x} (x - 6) = 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 - 6 )}{( 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 - 6 )}{( x ^{2} e ^{x} ) ^{2}} : \frac{- x ^{2} + 5 x + 12}{7 e ^{x} x ^{3}}

= \frac{- x ^{2} + 5 x + 12}{7 e ^{x} x ^{3}}

e^{x} y \cdot \frac{d y}{d x} = e^{- y} + e^{- 3 x - y}

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

\frac{d}{d z} (2 x y)

\frac{\partial}{\partial x} (\frac{x ^{1 - a}}{1 - a})

\int \frac{x ^{3} + 4 x ^{2} - 5}{x ^{3}} d x

What is the derivative of (x-6/(7x^2e^x)) ?
The derivative of (x-6/(7x^2e^x)) is (-x^2+5x+12)/(7e^xx^3)
What is the first derivative of (x-6/(7x^2e^x)) ?
The first derivative of (x-6/(7x^2e^x)) is (-x^2+5x+12)/(7e^xx^3)