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}})

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 y = 6 x e^{2 x}

\int \frac{13}{( x - 7 ) ( x + 6 )} d x

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