What is (\partial)/(\partial x)((e^x)/(x^2+10)) ?

The answer to (\partial)/(\partial x)((e^x)/(x^2+10)) is (e^x(x^2+10)-2xe^x)/((x^2+10)^2)

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(\partial)/(\partial x)((e^x)/(x^2+10))

\frac{\partial}{\partial x} (\frac{e ^{x}}{x ^{2} + 10})

\frac{e ^{x} ( x ^{2} + 10 ) - 2 x e ^{x}}{( x ^{2} + 10 ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{e ^{x}}{x ^{2} + 10})

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( e ^{x} ) ( x ^{2} + 10 ) - \frac{\partial}{\partial x} ( x ^{2} + 10 ) e ^{x}}{( x ^{2} + 10 ) ^{2}}

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

\frac{\partial}{\partial x} (x^{2} + 10) = 2 x

= \frac{e ^{x} ( x ^{2} + 10 ) - 2 x e ^{x}}{( x ^{2} + 10 ) ^{2}}

n = 0 \sum \infty \frac{2 n + 1}{n !}

- 2 e^{x + 2} + e^{- 5}

y^{^{'}} = \frac{4 x ^{5} e ^{\frac{y}{x}} + x ^{3} y ^{2}}{x ^{4} y}

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

\frac{d}{d x} (sin^{n} (x) cos (n) x)

What is (\partial)/(\partial x)((e^x)/(x^2+10)) ?
The answer to (\partial)/(\partial x)((e^x)/(x^2+10)) is (e^x(x^2+10)-2xe^x)/((x^2+10)^2)