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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} (9 ln (4 x))

x - 4

\frac{d}{d x} (e^{x^{y}})

\frac{d}{d x} (e^{x^{2}} sin (x^{3} - 2))

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

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