Mister Exam

Derivative of tgx+5log7^x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
              x   
tan(x) + 5*log (7)
$$5 \log{\left(7 \right)}^{x} + \tan{\left(x \right)}$$
tan(x) + 5*log(7)^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 a constant times a function is the constant times the derivative of the function.

      So, the result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       2           x               
1 + tan (x) + 5*log (7)*log(log(7))
$$5 \log{\left(7 \right)}^{x} \log{\left(\log{\left(7 \right)} \right)} + \tan^{2}{\left(x \right)} + 1$$
The second derivative [src]
  /       2   \               x       2        
2*\1 + tan (x)/*tan(x) + 5*log (7)*log (log(7))
$$2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + 5 \log{\left(7 \right)}^{x} \log{\left(\log{\left(7 \right)} \right)}^{2}$$
The third derivative [src]
               2                                                   
  /       2   \         2    /       2   \        x       3        
2*\1 + tan (x)/  + 4*tan (x)*\1 + tan (x)/ + 5*log (7)*log (log(7))
$$2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 5 \log{\left(7 \right)}^{x} \log{\left(\log{\left(7 \right)} \right)}^{3}$$