What is the derivative of (x^2-1/(e^x)) ?

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

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

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

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

\frac{2 x - x ^{2} + 1}{e ^{x}}

Solution steps

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

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

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

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

Simplify

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

= \frac{2 x - x ^{2} + 1}{e ^{x}}

\frac{d}{d x} (- 9 sin (x))

x \to - 1 lim (3 x - 2)

\frac{5}{x} (1.5)

n = 0 \sum \infty \frac{n + 1}{2 ^{n}}

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