What is (\partial)/(\partial y)(e^xy^3+2ye^{2x}) ?

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

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(\partial)/(\partial y)(e^xy^3+2ye^{2x})

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d y}{d x} = - \frac{y}{10}

f (x) = x^{2} - 8, (2, - 4)

\int tan (x) 1 + sec^{4} (x) d x

sin (a x)

\int tan^{5} (x) sec^{4} (x) d x

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