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

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

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

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

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\frac{d}{d x} (sin (x - \frac{π}{6}))

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

Solution steps

\frac{d}{d x} (sin (x - \frac{π}{6}))

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

(4 t^{4} + \frac{4}{t ^{4}})^{\frac{1}{4}}

(e^{2 x} + 4) \frac{d y}{d x} = y

f (x) = (cos (x))^{33} x

\frac{d}{d x} (sin (x) cos (y))

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