What is (\partial)/(\partial x)((e^x)/(y+x^7)) ?

The answer to (\partial)/(\partial x)((e^x)/(y+x^7)) is (e^x(y+x^7)-7x^6e^x)/((y+x^7)^2)

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(\partial)/(\partial x)((e^x)/(y+x^7))

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

\frac{e ^{x} ( y + x ^{7} ) - 7 x ^{6} e ^{x}}{( y + x ^{7} ) ^{2}}

Solution steps

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

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

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

\frac{\partial}{\partial x} (y + x^{7}) = 7 x^{6}

= \frac{e ^{x} ( y + x ^{7} ) - 7 x ^{6} e ^{x}}{( y + x ^{7} ) ^{2}}

4 x^{3} - 18 x^{2} - 48 x

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

2 y = x, \frac{y ^{2}}{2} = x

\frac{d}{d x} (arcsec (x + 2))

x \to \infty lim (\frac{1}{- x})

What is (\partial)/(\partial x)((e^x)/(y+x^7)) ?
The answer to (\partial)/(\partial x)((e^x)/(y+x^7)) is (e^x(y+x^7)-7x^6e^x)/((y+x^7)^2)