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Derivative of lnsin(x)-1/4cosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
              cos(x)
log(sin(x)) - ------
                4   
$$\log{\left(\sin{\left(x \right)} \right)} - \frac{\cos{\left(x \right)}}{4}$$
log(sin(x)) - cos(x)/4
Detail solution
  1. Differentiate term by term:

    1. Let .

    2. The derivative of is .

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of sine is cosine:

      The result of the chain rule is:

    4. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of cosine is negative sine:

      So, the result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
sin(x)   cos(x)
------ + ------
  4      sin(x)
$$\frac{\sin{\left(x \right)}}{4} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$
The second derivative [src]
                 2   
     cos(x)   cos (x)
-1 + ------ - -------
       4         2   
              sin (x)
$$\frac{\cos{\left(x \right)}}{4} - 1 - \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}$$
The third derivative [src]
                3              
  sin(x)   2*cos (x)   2*cos(x)
- ------ + --------- + --------
    4          3        sin(x) 
            sin (x)            
$$- \frac{\sin{\left(x \right)}}{4} + \frac{2 \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}}$$