What is (\partial)/(\partial x)(|4x^2-6yx|) ?

The answer to (\partial)/(\partial x)(|4x^2-6yx|) is ((4x^2-6xy)(8x-6y))/(|4x^2-6xy|)

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(\partial)/(\partial x)(|4x^2-6yx|)

\frac{\partial}{\partial x} (4 x^{2} - 6 y x)

\frac{( 4 x ^{2} - 6 x y ) ( 8 x - 6 y )}{∣ 4 x ^{2} - 6 x y ∣}

Solution steps

\frac{\partial}{\partial x} (4 x^{2} - 6 y x)

Treat

y

as a constant

Apply the chain rule:

\frac{4 x ^{2} - 6 y x}{∣ ( 4 x ^{2} - 6 y x ) ∣} \frac{\partial}{\partial x} (4 x^{2} - 6 y x)

= \frac{4 x ^{2} - 6 y x}{∣ ( 4 x ^{2} - 6 y x ) ∣} \frac{\partial}{\partial x} (4 x^{2} - 6 y x)

\frac{\partial}{\partial x} (4 x^{2} - 6 y x) = 8 x - 6 y

= \frac{4 x ^{2} - 6 y x}{∣ ( 4 x ^{2} - 6 y x ) ∣} (8 x - 6 y)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( 4 x ^{2} - 6 x y ) ( 8 x - 6 y )}{∣ 4 x ^{2} - 6 x y ∣}

x \to 2 - lim (3 ln (x))

\int \frac{4}{x ^{2} - 16} d x

\frac{\partial}{\partial x} (x + 3 x y^{2} + x^{2} y)

\frac{1}{s ( s + 1 ) ^{3}}

\frac{x ^{3}}{x - 1}

What is (\partial)/(\partial x)(|4x^2-6yx|) ?
The answer to (\partial)/(\partial x)(|4x^2-6yx|) is ((4x^2-6xy)(8x-6y))/(|4x^2-6xy|)