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Identical expressions
22sqrt2sinx-22x+ five ,5p+ twenty-one
22 square root of 2 sinus of x minus 22x plus 5,5p plus 21
22 square root of 2 sinus of x minus 22x plus five ,5p plus twenty minus one
22√2sinx-22x+5,5p+21
Similar expressions
22sqrt2sinx-22x+5,5p-21
22sqrt2sinx-22x-5,5p+21
22sqrt2sinx+22x+5,5p+21

The derivative of the function/ 22sqrt2sinx-22x+5,5p+21

Derivative of 22sqrt2sinx-22x+5,5p+21

The solution

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     __________          11*p     
22*\/ 2*sin(x)  - 22*x + ---- + 21
                          2

$$\left(\frac{11 p}{2} + \left(- 22 x + 22 \sqrt{2 \sin{\left(x \right)}}\right)\right) + 21$$

22*sqrt(2*sin(x)) - 22*x + 11*p/2 + 21

Detail solution

Differentiate $\left(\frac{11 p}{2} + \left(- 22 x + 22 \sqrt{2 \sin{\left(x \right)}}\right)\right) + 21$ term by term:
1. Differentiate $\frac{11 p}{2} + \left(- 22 x + 22 \sqrt{2 \sin{\left(x \right)}}\right)$ term by term:
  1. Differentiate $- 22 x + 22 \sqrt{2 \sin{\left(x \right)}}$ term by term:
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Let $u = 2 \sin{\left(x \right)}$ .
      2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 \sin{\left(x \right)}$ :
        
        The derivative of a constant times a function is the constant times the derivative of the function.
        
        The derivative of sine is cosine:
        
        $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
        
        So, the result is: $2 \cos{\left(x \right)}$
        
        The result of the chain rule is:
        
        $\frac{\sqrt{2} \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}}$
      So, the result is: $\frac{11 \sqrt{2} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}$
    2. 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: $-22$
    The result is: $-22 + \frac{11 \sqrt{2} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}$
  2. The derivative of the constant $\frac{11 p}{2}$ is zero.
  The result is: $-22 + \frac{11 \sqrt{2} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}$
2. The derivative of the constant $21$ is zero.
The result is: $-22 + \frac{11 \sqrt{2} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}$

The answer is:

$-22 + \frac{11 \sqrt{2} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}$

The first derivative [src]

           ___       
      11*\/ 2 *cos(x)
-22 + ---------------
           ________  
         \/ sin(x)

$$-22 + \frac{11 \sqrt{2} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}$$

Simplify

The second derivative [src]

          /                  2     \
      ___ |  ________     cos (x)  |
-11*\/ 2 *|\/ sin(x)  + -----------|
          |                  3/2   |
          \             2*sin   (x)/

$$- 11 \sqrt{2} \left(\sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{2 \sin^{\frac{3}{2}}{\left(x \right)}}\right)$$

Simplify

The third derivative [src]

         /         2   \       
     ___ |    3*cos (x)|       
11*\/ 2 *|2 + ---------|*cos(x)
         |        2    |       
         \     sin (x) /       
-------------------------------
              ________         
          4*\/ sin(x)

$$\frac{11 \sqrt{2} \left(2 + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{4 \sqrt{\sin{\left(x \right)}}}$$

Simplify

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Derivative of 22sqrt2sinx-22x+5,5p+21

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