What is (\partial)/(\partial x)(8x^3y^2+6xy^4) ?

The answer to (\partial)/(\partial x)(8x^3y^2+6xy^4) is 24y^2x^2+6y^4

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(\partial)/(\partial x)(8x^3y^2+6xy^4)

\frac{\partial}{\partial x} (8 x^{3} y^{2} + 6 x y^{4})

24 y^{2} x^{2} + 6 y^{4}

Solution steps

\frac{\partial}{\partial x} (8 x^{3} y^{2} + 6 x y^{4})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x^{3} y^{2}) + \frac{\partial}{\partial x} (6 x y^{4})

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

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

= 24 y^{2} x^{2} + 6 y^{4}

f (x) = x e^{y} - 5 y = 2 x - 6 - 2 e^{2}

\frac{e ^{x}}{x ^{2} + 1}

x \to h lim (x + h)

\frac{d}{d x} (\frac{6}{x ^{2} + 2})

\int_{1}^{7} x^{2} d x

What is (\partial)/(\partial x)(8x^3y^2+6xy^4) ?
The answer to (\partial)/(\partial x)(8x^3y^2+6xy^4) is 24y^2x^2+6y^4