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Popular >

derivative of y= x/(e^x)

Solution

derivative of

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

Solution

\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}}

Popular Examples

derivative of f(x)=(x^3+2)/3 derivative of

f (x) = \frac{x ^{3} + 2}{3}

slope of 3 slope

3

derivative of f(x)=sqrt(1-x)derivative of

f (x) = 1 - x

derivative of f(x)=4sin(x)-x,\at x=0 derivative of

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derivative of y=\sqrt[3]{x}derivative of

Frequently Asked Questions (FAQ)

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)