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cosx^2+x^2

Derivative of cosx^2+x^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2       2
cos (x) + x 
$$x^{2} + \cos^{2}{\left(x \right)}$$
Detail solution
  1. Differentiate term by term:

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of cosine is negative sine:

      The result of the chain rule is:

    4. Apply the power rule: goes to

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
2*x - 2*cos(x)*sin(x)
$$2 x - 2 \sin{\left(x \right)} \cos{\left(x \right)}$$
The second derivative [src]
  /       2         2   \
2*\1 + sin (x) - cos (x)/
$$2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)} + 1\right)$$
The third derivative [src]
8*cos(x)*sin(x)
$$8 \sin{\left(x \right)} \cos{\left(x \right)}$$
The graph
Derivative of cosx^2+x^2