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

The answer to (\partial)/(\partial x)(xy(2+x)(y-3)) is y(y-3)(2+2x)

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(\partial)/(\partial x)(xy(2+x)(y-3))

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

y (y - 3) (2 + 2 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 2 + x

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (2 + x) = 1

= y (y - 3) (1 \cdot (2 + x) + 1 \cdot x)

Simplify

= y (y - 3) (2 + 2 x)

x^{2} \frac{d y}{d x} = y - x y, y (- 1) = - 5

\frac{d}{d x} (7 e^{x} - (\frac{10}{x ^{4}}))

f (x) = \frac{2 - \frac{1}{x}}{x - 3}

x \to - 2 - lim (g (x))

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

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