What is the derivative of (e^x/(5-x)) ?

The derivative of (e^x/(5-x)) is (-e^xx+6e^x)/((5-x)^2)

What is the first derivative of (e^x/(5-x)) ?

The first derivative of (e^x/(5-x)) is (-e^xx+6e^x)/((5-x)^2)

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\frac{d}{d x} (\frac{e ^{x}}{5 - x})

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

Solution steps

\frac{d}{d x} (\frac{e ^{x}}{5 - x})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (5 - x) = - 1

= \frac{e ^{x} ( 5 - x ) - ( - 1 ) e ^{x}}{( 5 - x ) ^{2}}

Simplify

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

= \frac{- e ^{x} x + 6 e ^{x}}{( 5 - x ) ^{2}}

f (x) = ln (ln (x^{3} e^{- 3 x}))

\frac{\partial}{\partial y} (x^{2} y + y^{2} z + z^{2} x)

\frac{d ^{2}}{d x ^{2}} (\frac{3 x + 5}{2 x - 1})

y^{^{'}} + x y = x y^{- 2}

\frac{d}{d x} (12 x - 3 x^{2})

What is the derivative of (e^x/(5-x)) ?
The derivative of (e^x/(5-x)) is (-e^xx+6e^x)/((5-x)^2)
What is the first derivative of (e^x/(5-x)) ?
The first derivative of (e^x/(5-x)) is (-e^xx+6e^x)/((5-x)^2)