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Popular >

derivative of (1-x/(e^x))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(-ycos(-3x))

\frac{\partial}{\partial x} (- y cos (- 3 x))

sum from n=2 to infinity of ((n-1))/n

n = 2 \sum \infty \frac{( n - 1 )}{n}

derivative of-x^4+2x^3+4x^2 derivative of

- x^{4} + 2 x^{3} + 4 x^{2}

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\int 2^{l n (x)} d x

Frequently Asked Questions (FAQ)

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