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

The answer to (\partial)/(\partial x)(|x|y+2x) is (yx)/(|x|)+2

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(\partial)/(\partial x)(|x|y+2x)

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

\frac{y x}{∣ x ∣} + 2

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{y x}{∣ x ∣} + 2

\frac{d}{d x} (3 e^{- 2 x})

\int \frac{1 + x}{x} d x

5 x^{4} (9 - 7 x)^{7}

\int_{- π}^{π} 1

f (x) = x^{3} - 3 x^{2} - 8 x + 9

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