What is (\partial)/(\partial x)((e^x)/(y+x^3)) ?

The answer to (\partial)/(\partial x)((e^x)/(y+x^3)) is (e^x(y+x^3)-3x^2e^x)/((y+x^3)^2)

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(\partial)/(\partial x)((e^x)/(y+x^3))

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{3}})

\frac{e ^{x} ( y + x ^{3} ) - 3 x ^{2} e ^{x}}{( y + x ^{3} ) ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{3}})

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 ^{3} ) - \frac{\partial}{\partial x} ( y + x ^{3} ) e ^{x}}{( y + x ^{3} ) ^{2}}

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

\frac{\partial}{\partial x} (y + x^{3}) = 3 x^{2}

= \frac{e ^{x} ( y + x ^{3} ) - 3 x ^{2} e ^{x}}{( y + x ^{3} ) ^{2}}

\frac{d}{d x} (tan (\frac{π}{4}))

\int \frac{x ^{3}}{( x ^{2} + 4 ) ^{2}} d x

x \to \infty lim (x^{8})

\int \frac{1 - x ^{2}}{1 + x ^{2}} d x

\int 4 x - 15 x^{2} + e^{x} d x

What is (\partial)/(\partial x)((e^x)/(y+x^3)) ?
The answer to (\partial)/(\partial x)((e^x)/(y+x^3)) is (e^x(y+x^3)-3x^2e^x)/((y+x^3)^2)