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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d ^{2}}{d r ( θ ) d θ} (r (θ) cos (θ))

\int_{0}^{\frac{π}{3}} cos (2 x) d x

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

\int sin (x) + 5 d x

\int \frac{ln ( x )}{16} d x

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