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Popular Calculus >

derivative of f(x)=(x+6)/(e^x)

Solution

derivative of

f (x) = \frac{x + 6}{e ^{x}}

Solution

\frac{- x - 5}{e ^{x}}

Solution steps

\frac{d}{d x} (\frac{x + 6}{e ^{x}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 6 ) e ^{x} - \frac{d}{d x} ( e ^{x} ) ( x + 6 )}{( e ^{x} ) ^{2}}

\frac{d}{d x} (x + 6) = 1

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

= \frac{1 \cdot e ^{x} - e ^{x} ( x + 6 )}{( e ^{x} ) ^{2}}

Simplify

\frac{1 \cdot e ^{x} - e ^{x} ( x + 6 )}{( e ^{x} ) ^{2}} : \frac{- x - 5}{e ^{x}}

= \frac{- x - 5}{e ^{x}}

Graph

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\int \frac{1}{x ^{2} + 8 x} d x

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x+6)/(e^x) ?
The derivative of f(x)=(x+6)/(e^x) is (-x-5)/(e^x)
What is the first derivative of f(x)=(x+6)/(e^x) ?
The first derivative of f(x)=(x+6)/(e^x) is (-x-5)/(e^x)