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

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

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(\partial)/(\partial x)(x^2+xy^3)

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

2 x + y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x + y^{3}

\frac{d}{d x} (\frac{4 2}{3} x^{\frac{3}{2}} - 1)

\frac{d}{d x} (- \frac{1}{sin ( x )})

y^{^{''}} + 3 y^{^{'}} = sin (t), y (0) = 1, y^{^{'}} (0) = 2

\int sec (x) + tan (x) d x

\int x^{3} x^{4} - 1 d x

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