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

The derivative of y= x/((e^x)) is (1-x)/(e^x)

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

The first derivative of y= x/((e^x)) is (1-x)/(e^x)

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

(e^{t^{2}})^{^{'}}

y = \frac{2}{x - 8}, (10, 1)

\int \frac{2 x}{5 - x ^{4}} d x

y = 2 x - x^{2}, (2, 0)

\int_{- 1}^{1} x^{- 3} d x

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