Mister Exam

Derivative of pi/4cosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
pi       
--*cos(x)
4        
π4cos(x)\frac{\pi}{4} \cos{\left(x \right)}
(pi/4)*cos(x)
Detail solution
  1. 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:

      ddxcos(x)=sin(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

    So, the result is: πsin(x)4- \frac{\pi \sin{\left(x \right)}}{4}


The answer is:

πsin(x)4- \frac{\pi \sin{\left(x \right)}}{4}

The graph
02468-8-6-4-2-10102-2
The first derivative [src]
-pi*sin(x) 
-----------
     4     
πsin(x)4- \frac{\pi \sin{\left(x \right)}}{4}
The second derivative [src]
-pi*cos(x) 
-----------
     4     
πcos(x)4- \frac{\pi \cos{\left(x \right)}}{4}
The third derivative [src]
pi*sin(x)
---------
    4    
πsin(x)4\frac{\pi \sin{\left(x \right)}}{4}