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

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

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

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

2 y x + 3 y^{4}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y x + 3 y^{4}

x \to 0 lim (\frac{x}{e ^{- 3 x} - 1})

3 x^{^{'}} + 6 x = 4, x (0) = 2

\frac{d}{d x} (1100 x^{2} - 0.2 x)

sin (2 x)

\frac{d}{d x} (16 x)

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