Mister Exam

Derivative of 7-3^x+4tgx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
     x           
7 - 3  + 4*tan(x)
$$\left(7 - 3^{x}\right) + 4 \tan{\left(x \right)}$$
Detail solution
  1. Differentiate term by term:

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

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

        So, the result is:

      The result is:

    2. 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:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
         2       x       
4 + 4*tan (x) - 3 *log(3)
$$- 3^{x} \log{\left(3 \right)} + 4 \tan^{2}{\left(x \right)} + 4$$
The second derivative [src]
   x    2        /       2   \       
- 3 *log (3) + 8*\1 + tan (x)/*tan(x)
$$- 3^{x} \log{\left(3 \right)}^{2} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}$$
The third derivative [src]
               2                                        
  /       2   \     x    3            2    /       2   \
8*\1 + tan (x)/  - 3 *log (3) + 16*tan (x)*\1 + tan (x)/
$$- 3^{x} \log{\left(3 \right)}^{3} + 8 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 16 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}$$
The graph
Derivative of 7-3^x+4tgx