What is (\partial)/(\partial x)((x^{5/7})/(e^x)) ?

The answer to (\partial)/(\partial x)((x^{5/7})/(e^x)) is (5-7x)/(7e^xx^{2/7)}

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(\partial)/(\partial x)((x^{5/7})/(e^x))

\frac{\partial}{\partial x} (\frac{x ^{\frac{5}{7}}}{e ^{x}})

\frac{5 - 7 x}{7 e ^{x} x ^{\frac{2}{7}}}

Solution steps

\frac{\partial}{\partial x} (\frac{x ^{\frac{5}{7}}}{e ^{x}})

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( x ^{\frac{5}{7}} ) e ^{x} - \frac{\partial}{\partial x} ( e ^{x} ) x ^{\frac{5}{7}}}{( e ^{x} ) ^{2}}

\frac{\partial}{\partial x} (x^{\frac{5}{7}}) = \frac{5}{7 x ^{\frac{2}{7}}}

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

= \frac{\frac{5}{7 x ^{\frac{2}{7}}} e ^{x} - e ^{x} x ^{\frac{5}{7}}}{( e ^{x} ) ^{2}}

Simplify

\frac{\frac{5}{7 x ^{\frac{2}{7}}} e ^{x} - e ^{x} x ^{\frac{5}{7}}}{( e ^{x} ) ^{2}} : \frac{5 - 7 x}{7 e ^{x} x ^{\frac{2}{7}}}

= \frac{5 - 7 x}{7 e ^{x} x ^{\frac{2}{7}}}

x \to 0 lim (\frac{2}{x ^{2} + x} - \frac{2}{x})

\frac{3 t ^{2} + 4 t - 8}{t ^{\frac{3}{2}}}

x \to 0 lim (x^{3} - 4 x^{2} + 9 x - 2)

\int cos (2 x) d^{2} x d x

y^{^{''}} + 25 y = 0, y (0) = 4.6, y^{^{'}} (0) = - 1.2

What is (\partial)/(\partial x)((x^{5/7})/(e^x)) ?
The answer to (\partial)/(\partial x)((x^{5/7})/(e^x)) is (5-7x)/(7e^xx^{2/7)}