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

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

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

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

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derivative

\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}}

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