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The derivative of the function/ 2/3*tgx+sin*x/3

Derivative of 2/3*tgx+sin*x/3

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
2*tan(x)   sin(x)
-------- + ------
   3         3
$$\frac{\sin{\left(x \right)}}{3} + \frac{2 \tan{\left(x \right)}}{3}$$ 
2*tan(x)/3 + sin(x)/3
Detail solution

  1. Differentiate term by term:

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

      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:

      So, the result is:

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

      1. The derivative of sine is cosine:

      So, the result is:

    The result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                  2   
2   cos(x)   2*tan (x)
- + ------ + ---------
3     3          3
$$\frac{\cos{\left(x \right)}}{3} + \frac{2 \tan^{2}{\left(x \right)}}{3} + \frac{2}{3}$$
Simplify
The second derivative [src] 
            /       2   \       
-sin(x) + 4*\1 + tan (x)/*tan(x)
--------------------------------
               3
$$\frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \sin{\left(x \right)}}{3}$$
Simplify
The third derivative [src] 
                         2                          
            /       2   \         2    /       2   \
-cos(x) + 4*\1 + tan (x)/  + 8*tan (x)*\1 + tan (x)/
----------------------------------------------------
                         3
$$\frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} - \cos{\left(x \right)}}{3}$$
Simplify
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