What is the derivative of cos(x-pi/6) ?

The derivative of cos(x-pi/6) is -(sqrt(3))/2 sin(x)+1/2 cos(x)

What is the first derivative of cos(x-pi/6) ?

The first derivative of cos(x-pi/6) is -(sqrt(3))/2 sin(x)+1/2 cos(x)

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\frac{d}{d x} (cos (x - \frac{π}{6}))

- \frac{3}{2} sin (x) + \frac{1}{2} cos (x)

Solution steps

\frac{d}{d x} (cos (x - \frac{π}{6}))

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

What is the derivative of cos(x-pi/6) ?
The derivative of cos(x-pi/6) is -(sqrt(3))/2 sin(x)+1/2 cos(x)
What is the first derivative of cos(x-pi/6) ?
The first derivative of cos(x-pi/6) is -(sqrt(3))/2 sin(x)+1/2 cos(x)