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Derivative of:
Derivative of y=4+6x-3x^4
Derivative of √x+√x+√x
Derivative of x*e^(-2x)
Derivative of x+ln(x^2-4)
Identical expressions
eight (sin^2x-cos^2x)
8( sinus of squared x minus co sinus of e of squared x)
eight ( sinus of squared x minus co sinus of e of squared x)
8(sin2x-cos2x)
8sin2x-cos2x
8(sin²x-cos²x)
8(sin to the power of 2x-cos to the power of 2x)
8sin^2x-cos^2x
Similar expressions
8(sin^2x+cos^2x)

The derivative of the function/ 8(sin^2x-cos^2x)

Derivative of 8(sin^2x-cos^2x)

The solution

You have entered [src]

  /   2         2   \
8*\sin (x) - cos (x)/

$$8 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)$$

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

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}$ term by term:
  1. Let $u = \sin{\left(x \right)}$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(x \right)}$ :
    1. The derivative of sine is cosine:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    The result of the chain rule is:
    
    $2 \sin{\left(x \right)} \cos{\left(x \right)}$
  4. 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: $4 \sin{\left(x \right)} \cos{\left(x \right)}$
So, the result is: $32 \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

$16 \sin{\left(2 x \right)}$

The answer is:

$16 \sin{\left(2 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

32*cos(x)*sin(x)

$$32 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

   /   2         2   \
32*\cos (x) - sin (x)/

$$32 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)$$

Simplify

The third derivative [src]

-128*cos(x)*sin(x)

$$- 128 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify