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2(sinx^2-cosx^2)

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Derivative of:
Derivative of 2(sinx^2-cosx^2)
Derivative of (3x-1)^7
Derivative of sin^3(2x+1)
Derivative of 4sin2pit
Identical expressions
two (sinx^ two -cosx^ two)
2( sinus of x squared minus co sinus of e of x squared )
two ( sinus of x to the power of two minus co sinus of e of x to the power of two)
2(sinx2-cosx2)
2sinx2-cosx2
2(sinx²-cosx²)
2(sinx to the power of 2-cosx to the power of 2)
2sinx^2-cosx^2
Similar expressions
2(sinx^2+cosx^2)

The derivative of the function/ 2(sinx^2-cosx^2)

Derivative of 2(sinx^2-cosx^2)

The solution

You have entered [src]

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

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

d /  /   2         2   \\
--\2*\sin (x) - cos (x)//
dx

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

Transform

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

$4 \sin{\left(2 x \right)}$

The answer is:

$4 \sin{\left(2 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

8*cos(x)*sin(x)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

-32*cos(x)*sin(x)

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

Simplify

The graph

Derivative of 2(sinx^2-cosx^2)