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Derivative of:
Derivative of x/(e^x+1)
Derivative of (x+1)^1/3
Derivative of sin(4*x-1)^(3)
Derivative of sin(9x+2)
Identical expressions
a*(one -cos(two *x))
a multiply by (1 minus co sinus of e of (2 multiply by x))
a multiply by (one minus co sinus of e of (two multiply by x))
a(1-cos(2x))
a1-cos2x
Similar expressions
a*(1+cos(2*x))

The derivative of the function/ a*(1-cos(2*x))

Derivative of a(1-cos(2x))

The solution

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a*(1 - cos(2*x))

$$a \left(1 - \cos{\left(2 x \right)}\right)$$

a*(1 - cos(2*x))

Detail solution

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

The answer is:

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

The first derivative [src]

2*a*sin(2*x)

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

Simplify

The second derivative [src]

4*a*cos(2*x)

$$4 a \cos{\left(2 x \right)}$$

Simplify

The third derivative [src]

-8*a*sin(2*x)

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

Simplify