What is the derivative of (e^x/(4-x)) ?

The derivative of (e^x/(4-x)) is (-e^xx+5e^x)/((4-x)^2)

What is the first derivative of (e^x/(4-x)) ?

The first derivative of (e^x/(4-x)) is (-e^xx+5e^x)/((4-x)^2)

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\frac{d}{d x} (\frac{e ^{x}}{4 - x})

\frac{- e ^{x} x + 5 e ^{x}}{( 4 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{4 - x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{x} ) ( 4 - x ) - \frac{d}{d x} ( 4 - x ) e ^{x}}{( 4 - x ) ^{2}}

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

\frac{d}{d x} (4 - x) = - 1

= \frac{e ^{x} ( 4 - x ) - ( - 1 ) e ^{x}}{( 4 - x ) ^{2}}

Simplify

\frac{e ^{x} ( 4 - x ) - ( - 1 ) e ^{x}}{( 4 - x ) ^{2}} : \frac{- e ^{x} x + 5 e ^{x}}{( 4 - x ) ^{2}}

= \frac{- e ^{x} x + 5 e ^{x}}{( 4 - x ) ^{2}}

y^{^{''}} - 2 y^{^{'}} + y = t e^{t}

\int p (p + 5)^{5} d p

x \to \infty lim (\frac{1}{2} x)

\frac{1}{3} x^{3} - 3 x^{2} + 10 x + 6, at x = 2

\frac{x d y}{d x} = y

What is the derivative of (e^x/(4-x)) ?
The derivative of (e^x/(4-x)) is (-e^xx+5e^x)/((4-x)^2)
What is the first derivative of (e^x/(4-x)) ?
The first derivative of (e^x/(4-x)) is (-e^xx+5e^x)/((4-x)^2)