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Derivative of:
Derivative of y=2x-1
Derivative of x-ln(1+x)
Derivative of x*(1-x)
Derivative of f(x)=1/4x^4+x
Identical expressions
one / two *sin(2x- one)
1 divide by 2 multiply by sinus of (2x minus 1)
one divide by two multiply by sinus of (2x minus one)
1/2sin(2x-1)
1/2sin2x-1
1 divide by 2*sin(2x-1)
Similar expressions
1/2*sin(2x+1)

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

Derivative of 1/2*sin(2x-1)

The solution

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sin(2*x - 1)
------------
     2

$$\frac{\sin{\left(2 x - 1 \right)}}{2}$$

sin(2*x - 1)/2

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

cos(2*x - 1)

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

Simplify

The second derivative [src]

-2*sin(-1 + 2*x)

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

Simplify

The third derivative [src]

-4*cos(-1 + 2*x)

$$- 4 \cos{\left(2 x - 1 \right)}$$

Simplify