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

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

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

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

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

Solution steps

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

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

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

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

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

x \to 2 lim (\frac{4}{x - 2})

t \to 0 lim (e^{- 2 t})

\frac{d}{d x} (\frac{2 ( - x ^{2} - 1 )}{( x ^{2} - 1 ) ^{2}})

n = 1 \sum \infty ln (\frac{n}{3 n + 1})

\int \frac{3}{x ^{- 1} + 3} d x

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