What is (\partial)/(\partial x)(4x^2y+7xy^3) ?

The answer to (\partial)/(\partial x)(4x^2y+7xy^3) is 8yx+7y^3

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(\partial)/(\partial x)(4x^2y+7xy^3)

\frac{\partial}{\partial x} (4 x^{2} y + 7 x y^{3})

8 y x + 7 y^{3}

Solution steps

\frac{\partial}{\partial x} (4 x^{2} y + 7 x y^{3})

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} (7 x y^{3})

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

\frac{\partial}{\partial x} (7 x y^{3}) = 7 y^{3}

= 8 y x + 7 y^{3}

f (x) = (3 x - 2) (4 x^{3} - x^{2} + 1)

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

x \to 2 lim (x^{2} - 6 x + 3)

\frac{d}{d x} (\frac{1}{1 + e ^{0.5 x}})

n = 1 \sum \infty n e^{- 6 n}

What is (\partial)/(\partial x)(4x^2y+7xy^3) ?
The answer to (\partial)/(\partial x)(4x^2y+7xy^3) is 8yx+7y^3