What is (\partial)/(\partial y)((e^y)/(x+y^9)) ?

The answer to (\partial)/(\partial y)((e^y)/(x+y^9)) is (e^y(x+y^9)-9y^8e^y)/((x+y^9)^2)

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(\partial)/(\partial y)((e^y)/(x+y^9))

\frac{\partial}{\partial y} (\frac{e ^{y}}{x + y ^{9}})

\frac{e ^{y} ( x + y ^{9} ) - 9 y ^{8} e ^{y}}{( x + y ^{9} ) ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{e ^{y}}{x + y ^{9}})

Treat

x

as a constant

Apply the Quotient Rule:

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

= \frac{\frac{\partial}{\partial y} ( e ^{y} ) ( x + y ^{9} ) - \frac{\partial}{\partial y} ( x + y ^{9} ) e ^{y}}{( x + y ^{9} ) ^{2}}

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

\frac{\partial}{\partial y} (x + y^{9}) = 9 y^{8}

= \frac{e ^{y} ( x + y ^{9} ) - 9 y ^{8} e ^{y}}{( x + y ^{9} ) ^{2}}

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

f (x) = cos (x) - sin (x)

n = 0 \sum \infty \frac{2 n}{n} x^{n}

\frac{\partial}{\partial x} (e^{x} sin (y + z) - z)

x \to 4 lim (3 - 2)

What is (\partial)/(\partial y)((e^y)/(x+y^9)) ?
The answer to (\partial)/(\partial y)((e^y)/(x+y^9)) is (e^y(x+y^9)-9y^8e^y)/((x+y^9)^2)