What is (\partial)/(\partial x)((e^x)/(y+x^8)) ?

The answer to (\partial)/(\partial x)((e^x)/(y+x^8)) is (e^x(y+x^8)-8x^7e^x)/((y+x^8)^2)

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(\partial)/(\partial x)((e^x)/(y+x^8))

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{8}})

\frac{e ^{x} ( y + x ^{8} ) - 8 x ^{7} e ^{x}}{( y + x ^{8} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{8}})

Treat

y

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial x} ( e ^{x} ) ( y + x ^{8} ) - \frac{\partial}{\partial x} ( y + x ^{8} ) e ^{x}}{( y + x ^{8} ) ^{2}}

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

\frac{\partial}{\partial x} (y + x^{8}) = 8 x^{7}

= \frac{e ^{x} ( y + x ^{8} ) - 8 x ^{7} e ^{x}}{( y + x ^{8} ) ^{2}}

\frac{d}{d x} (\frac{x + y}{x y})

y^{^{'}} = 1 - \frac{y}{20}

7 x^{2} y^{^{'}} = y^{^{'}} + 9 x e - y

\int_{1}^{\infty} \frac{1}{x ^{2} + x} d x

\frac{d}{d x} (2^{x} ln^{2} (2))

What is (\partial)/(\partial x)((e^x)/(y+x^8)) ?
The answer to (\partial)/(\partial x)((e^x)/(y+x^8)) is (e^x(y+x^8)-8x^7e^x)/((y+x^8)^2)