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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d y}{d x} = 1 - 2 y

\int tan^{5} (8 x) sec^{4} (8 x) d x

f (x) = \frac{1}{3 x}

(4 x)^{10 x^{3}}

\frac{d}{d x} (\frac{1}{sinh ( x )})

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