What is (\partial)/(\partial x)(|3x+y-4|) ?

The answer to (\partial)/(\partial x)(|3x+y-4|) is (3(3x+y-4))/(|3x+y-4|)

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(\partial)/(\partial x)(|3x+y-4|)

\frac{\partial}{\partial x} (∣ 3 x + y - 4 ∣)

\frac{3 ( 3 x + y - 4 )}{∣ 3 x + y - 4 ∣}

Solution steps

\frac{\partial}{\partial x} (∣ 3 x + y - 4 ∣)

Treat

y

as a constant

Apply the chain rule:

\frac{3 x + y - 4}{∣ ( 3 x + y - 4 ) ∣} \frac{\partial}{\partial x} (3 x + y - 4)

= \frac{3 x + y - 4}{∣ ( 3 x + y - 4 ) ∣} \frac{\partial}{\partial x} (3 x + y - 4)

\frac{\partial}{\partial x} (3 x + y - 4) = 3

= \frac{3 x + y - 4}{∣ ( 3 x + y - 4 ) ∣} \cdot 3

Multiply fractions:

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

= \frac{3 ( 3 x + y - 4 )}{∣ 3 x + y - 4 ∣}

x \to 6 lim (36 - x^{2})

\int_{1}^{2} x (x^{2} + 1)^{2} d x

\frac{d v}{d t} = \frac{( 10 - v )}{1}

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

\int 16 - y d y

What is (\partial)/(\partial x)(|3x+y-4|) ?
The answer to (\partial)/(\partial x)(|3x+y-4|) is (3(3x+y-4))/(|3x+y-4|)