What is the derivative of f(x)=(e^xx-e^x)/(5x^2) ?

The derivative of f(x)=(e^xx-e^x)/(5x^2) is (e^x(x^2-2(x-1)))/(5x^3)

What is the first derivative of f(x)=(e^xx-e^x)/(5x^2) ?

The first derivative of f(x)=(e^xx-e^x)/(5x^2) is (e^x(x^2-2(x-1)))/(5x^3)

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derivative of

f (x) = \frac{e ^{x} x - e ^{x}}{5 x ^{2}}

\frac{e ^{x} ( x ^{2} - 2 ( x - 1 ) )}{5 x ^{3}}

Solution steps

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

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{e ^{x} x - e ^{x}}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( e ^{x} x - e ^{x} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( e ^{x} x - e ^{x} )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (e^{x} x - e^{x}) = e^{x} x

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

= \frac{1}{5} \cdot \frac{e ^{x} x x ^{2} - 2 x ( e ^{x} x - e ^{x} )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{5} \cdot \frac{e ^{x} x x ^{2} - 2 x ( e ^{x} x - e ^{x} )}{( x ^{2} ) ^{2}} : \frac{e ^{x} ( x ^{2} - 2 ( x - 1 ) )}{5 x ^{3}}

= \frac{e ^{x} ( x ^{2} - 2 ( x - 1 ) )}{5 x ^{3}}

\int \frac{e ^{x} + 1}{e ^{x}} d x

\frac{3 x - 7}{x}

\frac{d y}{d x} = - 6 y x

x \to 7 lim (\frac{x}{x ^{2} - 49})

What is the derivative of f(x)=(e^xx-e^x)/(5x^2) ?
The derivative of f(x)=(e^xx-e^x)/(5x^2) is (e^x(x^2-2(x-1)))/(5x^3)
What is the first derivative of f(x)=(e^xx-e^x)/(5x^2) ?
The first derivative of f(x)=(e^xx-e^x)/(5x^2) is (e^x(x^2-2(x-1)))/(5x^3)