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

The answer to (\partial)/(\partial x)(2x^3+2xy^3) is 6x^2+2y^3

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

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

= 6 x^{2} + 2 y^{3}

\int \frac{1}{16 x} d x

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

g (x) = \frac{( π ^{2} )}{x ^{2} + 4 x}

\frac{d}{d x} (sec (x) - x)

y = x^{2} + 4 x - 11, (2, - 1)

What is (\partial)/(\partial x)(2x^3+2xy^3) ?
The answer to (\partial)/(\partial x)(2x^3+2xy^3) is 6x^2+2y^3