What is the derivative of 12cos(2x+pi/6) ?

The derivative of 12cos(2x+pi/6) is 12(-sqrt(3)sin(2x)-cos(2x))

What is the first derivative of 12cos(2x+pi/6) ?

The first derivative of 12cos(2x+pi/6) is 12(-sqrt(3)sin(2x)-cos(2x))

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\frac{d}{d x} (12 cos (2 x + \frac{π}{6}))

12 (- 3 sin (2 x) - cos (2 x))

Solution steps

\frac{d}{d x} (12 cos (2 x + \frac{π}{6}))

Simplify

12 cos (2 x + \frac{π}{6}) : 12 (\frac{3}{2} cos (2 x) - \frac{1}{2} sin (2 x))

= \frac{d}{d x} (12 (\frac{3}{2} cos (2 x) - \frac{1}{2} sin (2 x)))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d x} (\frac{3}{2} cos (2 x) - \frac{1}{2} sin (2 x))

Apply the Sum/Difference Rule:

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

= 12 (\frac{d}{d x} (\frac{3}{2} cos (2 x)) - \frac{d}{d x} (\frac{1}{2} sin (2 x)))

\frac{d}{d x} (\frac{3}{2} cos (2 x)) = - 3 sin (2 x)

\frac{d}{d x} (\frac{1}{2} sin (2 x)) = cos (2 x)

= 12 (- 3 sin (2 x) - cos (2 x))

What is the derivative of 12cos(2x+pi/6) ?
The derivative of 12cos(2x+pi/6) is 12(-sqrt(3)sin(2x)-cos(2x))
What is the first derivative of 12cos(2x+pi/6) ?
The first derivative of 12cos(2x+pi/6) is 12(-sqrt(3)sin(2x)-cos(2x))