What is the derivative of (x^2+5/(e^x)) ?

The derivative of (x^2+5/(e^x)) is (2x-x^2-5)/(e^x)

What is the first derivative of (x^2+5/(e^x)) ?

The first derivative of (x^2+5/(e^x)) is (2x-x^2-5)/(e^x)

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

\frac{2 x - x ^{2} - 5}{e ^{x}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{2} + 5) = 2 x

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

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

Simplify

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

= \frac{2 x - x ^{2} - 5}{e ^{x}}

\frac{s + 3}{s ^{2} + 4 s + 4}

\frac{1}{1 + 2 x ^{3}}

\int sec^{14} (x) tan (x) d x

\frac{d}{d x} (\frac{12}{x ^{5}})

\int sin (t) d t

What is the derivative of (x^2+5/(e^x)) ?
The derivative of (x^2+5/(e^x)) is (2x-x^2-5)/(e^x)
What is the first derivative of (x^2+5/(e^x)) ?
The first derivative of (x^2+5/(e^x)) is (2x-x^2-5)/(e^x)