What is (\partial)/(\partial x)((5x)/(e^x)) ?

The answer to (\partial)/(\partial x)((5x)/(e^x)) is (5(1-x))/(e^x)

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(\partial)/(\partial x)((5x)/(e^x))

\frac{\partial}{\partial x} (\frac{5 x}{e ^{x}})

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

Solution steps

\frac{\partial}{\partial x} (\frac{5 x}{e ^{x}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \frac{\partial}{\partial x} (\frac{x}{e ^{x}})

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

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

\int \frac{x ^{3} + 2 x}{x ^{2} - 1} d x

\frac{d}{d x} (- \frac{3}{4} x^{- \frac{2}{3}})

\int \frac{7}{4 x ^{3}} d x

t y^{^{'}} - y = \frac{- t ^{3}}{y ^{2}}, y (1) = 2

\int_{0}^{3} (3 t - 5) d t

What is (\partial)/(\partial x)((5x)/(e^x)) ?
The answer to (\partial)/(\partial x)((5x)/(e^x)) is (5(1-x))/(e^x)