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

The answer to (\partial)/(\partial x)(x^2y+4x^4y) is 2yx+16yx^3

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

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

2 y x + 16 y x^{3}

Solution steps

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

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} (4 x^{4} y)

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

\frac{\partial}{\partial x} (4 x^{4} y) = 16 y x^{3}

= 2 y x + 16 y x^{3}

n = 3 \sum \infty \frac{1}{n ( n + 1 )}

\int \frac{a e ^{θ} + b}{a e ^{θ} - b} d θ

y = \frac{1}{1 + e ^{- x}}

\frac{\partial}{\partial x} (e^{2 x} sin (2 y))

x \to 2 lim (\frac{x ^{2} - 4}{x + 2})

What is (\partial)/(\partial x)(x^2y+4x^4y) ?
The answer to (\partial)/(\partial x)(x^2y+4x^4y) is 2yx+16yx^3