What is (\partial)/(\partial x)(6xy^2-2x^3-3y^4) ?

The answer to (\partial)/(\partial x)(6xy^2-2x^3-3y^4) is 6y^2-6x^2

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(\partial)/(\partial x)(6xy^2-2x^3-3y^4)

\frac{\partial}{\partial x} (6 x y^{2} - 2 x^{3} - 3 y^{4})

6 y^{2} - 6 x^{2}

Solution steps

\frac{\partial}{\partial x} (6 x y^{2} - 2 x^{3} - 3 y^{4})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x y^{2}) - \frac{\partial}{\partial x} (2 x^{3}) - \frac{\partial}{\partial x} (3 y^{4})

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

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

\frac{\partial}{\partial x} (3 y^{4}) = 0

= 6 y^{2} - 6 x^{2} - 0

Simplify

= 6 y^{2} - 6 x^{2}

\frac{d ^{2} y}{d x ^{2}} = 3

\frac{\partial}{\partial x} (2 x + 4 y)

\frac{d}{d x} (2 x \cdot e^{x})

\int \frac{1}{4 sin ( x )} d x

x \to 0 lim (lo g_{\frac{2}{3}} (x))

What is (\partial)/(\partial x)(6xy^2-2x^3-3y^4) ?
The answer to (\partial)/(\partial x)(6xy^2-2x^3-3y^4) is 6y^2-6x^2