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The derivative of the function/ cos(x+pi/6)

Derivative of cos(x+pi/6)

Function f() - derivative -N order at the point
v

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The solution

You have entered [src] 
   /    pi\
cos|x + --|
   \    6 /
cos⁡(x+π6)\cos{\left(x + \frac{\pi}{6} \right)} 
cos(x + pi/6)
Detail solution

  1. Let u=x+π6u = x + \frac{\pi}{6}.

  2. The derivative of cosine is negative sine:

    dducos⁡(u)=−sin⁡(u)\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}

  3. Then, apply the chain rule. Multiply by ddx(x+π6)\frac{d}{d x} \left(x + \frac{\pi}{6}\right):

    1. Differentiate x+π6x + \frac{\pi}{6} term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant π6\frac{\pi}{6} is zero.

      The result is: 11

    The result of the chain rule is:

    −sin⁡(x+π6)- \sin{\left(x + \frac{\pi}{6} \right)}

  4. Now simplify:

    −sin⁡(x+π6)- \sin{\left(x + \frac{\pi}{6} \right)}

The answer is:

−sin⁡(x+π6)- \sin{\left(x + \frac{\pi}{6} \right)}

The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    /    pi\
-sin|x + --|
    \    6 /
−sin⁡(x+π6)- \sin{\left(x + \frac{\pi}{6} \right)}
Simplify
The second derivative [src] 
    /    pi\
-cos|x + --|
    \    6 /
−cos⁡(x+π6)- \cos{\left(x + \frac{\pi}{6} \right)}
Simplify
The third derivative [src] 
   /    pi\
sin|x + --|
   \    6 /
sin⁡(x+π6)\sin{\left(x + \frac{\pi}{6} \right)}
Simplify
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