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cosx^ two +x^ two
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Similar expressions
cosx^2-x^2

The derivative of the function/ cosx^2+x^2

Derivative of cosx^2+x^2

The solution

You have entered [src]

   2       2
cos (x) + x

$$x^{2} + \cos^{2}{\left(x \right)}$$

Transform

Detail solution

Differentiate $x^{2} + \cos^{2}{\left(x \right)}$ term by term:
1. Let $u = \cos{\left(x \right)}$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(x \right)}$ :
  1. The derivative of cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  The result of the chain rule is:
  
  $- 2 \sin{\left(x \right)} \cos{\left(x \right)}$
4. Apply the power rule: $x^{2}$ goes to $2 x$
The result is: $2 x - 2 \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

$2 x - \sin{\left(2 x \right)}$

The answer is:

$2 x - \sin{\left(2 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*x - 2*cos(x)*sin(x)

$$2 x - 2 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

  /       2         2   \
2*\1 + sin (x) - cos (x)/

$$2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)} + 1\right)$$

Simplify

The third derivative [src]

8*cos(x)*sin(x)

$$8 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The graph

Derivative of cosx^2+x^2