What is (\partial)/(\partial x)(8xy^2-8x^3y) ?

The answer to (\partial)/(\partial x)(8xy^2-8x^3y) is 8y^2-24yx^2

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(\partial)/(\partial x)(8xy^2-8x^3y)

\frac{\partial}{\partial x} (8 x y^{2} - 8 x^{3} y)

8 y^{2} - 24 y x^{2}

Solution steps

\frac{\partial}{\partial x} (8 x y^{2} - 8 x^{3} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x y^{2}) - \frac{\partial}{\partial x} (8 x^{3} y)

\frac{\partial}{\partial x} (8 x y^{2}) = 8 y^{2}

\frac{\partial}{\partial x} (8 x^{3} y) = 24 y x^{2}

= 8 y^{2} - 24 y x^{2}

\int \frac{1}{sin ^{4} ( x ) cos ^{2} ( x )} d x

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

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

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

f (x) = 7 - x^{2}

What is (\partial)/(\partial x)(8xy^2-8x^3y) ?
The answer to (\partial)/(\partial x)(8xy^2-8x^3y) is 8y^2-24yx^2