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

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

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

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

8 y x + 6 y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 8 y x + 6 y^{2}

\frac{d}{d x} (\frac{7 x}{x ^{2} + 4})

\frac{1}{6} x^{3} + \frac{1}{2 x}

\frac{d}{d x} (4 + 3 f (x))

x \to 0 + lim (ln (\frac{9}{x ^{3}}))

\frac{d}{d x} (cos^{2} (ln (e^{2 x + 1} (- 2 x))))

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