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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derivative of

\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}}

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

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

\int \frac{1 - cos ( x )}{1 + sin ( x )} d x

f (x) = \frac{x ^{2}}{( x - 2 ) ^{2}}

y^{^{''}} + 16 y^{^{'}} = 0

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)