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

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

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(\partial)/(\partial x)(y-2ln|y|+xy)

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

y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (y) = 0

\frac{\partial}{\partial x} (2 ln ∣ y ∣) = 0

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

= 0 - 0 + y

Simplify

= y

\int x \cdot e^{- 2 x^{2}} d x

\frac{d}{d x} (a x + b)

\frac{d}{d x} (\frac{2 x ^{2}}{4 - x ^{2}})

\int_{2}^{4} (x - 9) d x

\int \frac{1}{x ^{2} + x ^{3}} d x

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