What is (\partial)/(\partial x)((x)(2xy)) ?

The answer to (\partial)/(\partial x)((x)(2xy)) is 4xy

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(\partial)/(\partial x)((x)(2xy))

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

4 x y

Solution steps

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

Simplify

(x) (2 x y) : 2 x^{2} y

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 y \cdot 2 x^{2 - 1}

Simplify

= 4 x y

\frac{d y}{d x} = \frac{7 x}{4 y}

\int \frac{3}{cos ^{2} ( x )} d x

\frac{\partial}{\partial s} (\frac{3 r + s}{t})

\frac{d ^{2} y}{d x ^{2}} + 4 \frac{d y}{d x} + 5 y = 0

\int_{0}^{2 π} ∣ cos (x) ∣ d x

What is (\partial)/(\partial x)((x)(2xy)) ?
The answer to (\partial)/(\partial x)((x)(2xy)) is 4xy