Mister Exam

Derivative of cosecxtanx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
cos(e)*c*x*tan(x)
$$c x \cos{\left(e \right)} \tan{\left(x \right)}$$
d                    
--(cos(e)*c*x*tan(x))
dx                   
$$\frac{\partial}{\partial x} c x \cos{\left(e \right)} \tan{\left(x \right)}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Apply the product rule:

      ; to find :

      1. Apply the power rule: goes to

      ; to find :

      1. Rewrite the function to be differentiated:

      2. Apply the quotient rule, which is:

        and .

        To find :

        1. The derivative of sine is cosine:

        To find :

        1. The derivative of cosine is negative sine:

        Now plug in to the quotient rule:

      The result is:

    So, the result is:

  2. Now simplify:


The answer is:

The first derivative [src]
                      /       2   \       
c*cos(e)*tan(x) + c*x*\1 + tan (x)/*cos(e)
$$c x \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(e \right)} + c \cos{\left(e \right)} \tan{\left(x \right)}$$
The second derivative [src]
    /       2   \                      
2*c*\1 + tan (x)/*(1 + x*tan(x))*cos(e)
$$2 c \left(x \tan{\left(x \right)} + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(e \right)}$$
The third derivative [src]
    /       2   \ /             /         2   \\       
2*c*\1 + tan (x)/*\3*tan(x) + x*\1 + 3*tan (x)//*cos(e)
$$2 c \left(x \left(3 \tan^{2}{\left(x \right)} + 1\right) + 3 \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(e \right)}$$