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

The derivative of (xe^x-e^x/(x^2)) is (e^x(x^2-2(x-1)))/(x^3)

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

The first derivative of (xe^x-e^x/(x^2)) is (e^x(x^2-2(x-1)))/(x^3)

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Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 0 lim (3 x + 1)

\frac{4}{x - 7}

\frac{\partial}{\partial x} (x^{2} + 2 x y - y^{2} - 8 x)

f (t) = - 4 t^{2} + 16 t + 9

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

What is the derivative of (xe^x-e^x/(x^2)) ?
The derivative of (xe^x-e^x/(x^2)) is (e^x(x^2-2(x-1)))/(x^3)
What is the first derivative of (xe^x-e^x/(x^2)) ?
The first derivative of (xe^x-e^x/(x^2)) is (e^x(x^2-2(x-1)))/(x^3)