Mister Exam

Derivative of xtanx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
x*tan(x)
$$x \tan{\left(x \right)}$$
d           
--(x*tan(x))
dx          
$$\frac{d}{d x} x \tan{\left(x \right)}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    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:

    The result is:

  2. Now simplify:


The answer is:

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