What is the derivative of |sin(6x|) ?

The derivative of |sin(6x|) is (3sin(12x))/(|sin(6x)|)

What is the first derivative of |sin(6x|) ?

The first derivative of |sin(6x|) is (3sin(12x))/(|sin(6x)|)

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\frac{d}{d x} (∣ sin (6 x) ∣)

\frac{3 sin ( 12 x )}{∣ sin ( 6 x ) ∣}

Solution steps

\frac{d}{d x} (∣ sin (6 x) ∣)

Apply the chain rule:

\frac{sin ( 6 x )}{∣ sin ( 6 x ) ∣} \frac{d}{d x} (sin (6 x))

= \frac{sin ( 6 x )}{∣ sin ( 6 x ) ∣} \frac{d}{d x} (sin (6 x))

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

= \frac{sin ( 6 x )}{∣ sin ( 6 x ) ∣} cos (6 x) \cdot 6

Simplify

\frac{sin ( 6 x )}{∣ sin ( 6 x ) ∣} cos (6 x) \cdot 6 : \frac{3 sin ( 12 x )}{∣ sin ( 6 x ) ∣}

= \frac{3 sin ( 12 x )}{∣ sin ( 6 x ) ∣}

What is the derivative of |sin(6x|) ?
The derivative of |sin(6x|) is (3sin(12x))/(|sin(6x)|)
What is the first derivative of |sin(6x|) ?
The first derivative of |sin(6x|) is (3sin(12x))/(|sin(6x)|)