Mister Exam

Derivative of (tg(x))+(sin(x))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
tan(x) + sin(x)
$$\sin{\left(x \right)} + \tan{\left(x \right)}$$
tan(x) + sin(x)
Detail solution
  1. Differentiate term by term:

    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:

    3. The derivative of sine is cosine:

    The result is:

  2. Now simplify:


The answer is:

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