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

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

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

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

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

Solution steps

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

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

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

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

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

y^{^{'}} = \frac{( ( y - y ^{2} ) t )}{1 + t ^{2}}, y (0) = \frac{1}{2}

\int 2 t^{\frac{3}{2}} d t

\int \frac{9}{( x - 7 ) ( x + 2 )} d x

\frac{d x}{d t} = x b

2 x^{3} e^{- x}

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