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Derivative of:
Derivative of f(x)=x
Derivative of sin^2(x/2)
Derivative of sin(2*x)^(2)
Derivative of 2*cos(3*x)
Identical expressions
y=x^ two -cos^2x
y equally x squared minus co sinus of e of squared x
y equally x to the power of two minus co sinus of e of squared x
y=x2-cos2x
y=x²-cos²x
y=x to the power of 2-cos to the power of 2x
Similar expressions
y=x^2+cos^2x

The derivative of the function/ y=x^2-cos^2x

Derivative of y=x^2-cos^2x

The solution

You have entered [src]

 2      2   
x  - cos (x)

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

x^2 - cos(x)^2

Detail solution

Differentiate $x^{2} - \cos^{2}{\left(x \right)}$ term by term:
1. Apply the power rule: $x^{2}$ goes to $2 x$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  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:
    
    $- 2 \sin{\left(x \right)} \cos{\left(x \right)}$
  So, the result is: $2 \sin{\left(x \right)} \cos{\left(x \right)}$
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 + cos (x) - sin (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 y=x^2-cos^2x