Mister Exam

Derivative of log(4)log(2)tgx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(4)*log(2)*tan(x)
$$\log{\left(2 \right)} \log{\left(4 \right)} \tan{\left(x \right)}$$
d                       
--(log(4)*log(2)*tan(x))
dx                      
$$\frac{d}{d x} \log{\left(2 \right)} \log{\left(4 \right)} \tan{\left(x \right)}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. 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. Now simplify:


The answer is:

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