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

The answer to (\partial)/(\partial x)(x-2|x-2/3 y|) is 1-(2(3x-2y))/(|3x-2y|)

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(\partial)/(\partial x)(x-2|x-2/3 y|)

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

1 - \frac{2 ( 3 x - 2 y )}{∣ 3 x - 2 y ∣}

Solution steps

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

Simplify

x - 2 x - \frac{2}{3} y : x - 2 x - \frac{2 y}{3}

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

f (x) = x^{4} + 3 x

\frac{1}{1 - 2 x}

(sin (x) + x cos (x))^{^{'}}

\int \frac{2 e ^{2 x}}{e ^{10} - 1} d x

\int \frac{1}{( 121 + x ^{2} ) ^{2}} d x

What is (\partial)/(\partial x)(x-2|x-2/3 y|) ?
The answer to (\partial)/(\partial x)(x-2|x-2/3 y|) is 1-(2(3x-2y))/(|3x-2y|)