What is (\partial)/(\partial y)(y^3+2ye^x) ?

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

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(\partial)/(\partial y)(y^3+2ye^x)

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

3 y^{2} + 2 e^{x}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= 3 y^{2} + 2 e^{x}

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

\frac{\partial}{\partial y} (\frac{100}{5 x ^{2} + y ^{2}})

\frac{s}{s ^{2} + 4 s}

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

\frac{\partial}{\partial x} (5 x^{5} y^{8} + 8 x^{6} y^{7})

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