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Identical expressions
three -5pi/ four +5x-5sqrt2sinx
3 minus 5 Pi divide by 4 plus 5x minus 5 square root of 2 sinus of x
three minus 5 Pi divide by four plus 5x minus 5 square root of 2 sinus of x
3-5pi/4+5x-5√2sinx
3-5pi divide by 4+5x-5sqrt2sinx
Similar expressions
(3-((5*pi)/4)+(5*x)-(5*sqrt(2)*sinx))
3+5pi/4+5x-5sqrt2sinx
3-5pi/4+5x+5sqrt2sinx
3-5pi/4-5x-5sqrt2sinx

The derivative of the function/ 3-5pi/4+5x-5sqrt2sinx

Derivative of 3-5pi/4+5x-5sqrt2sinx

The solution

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    5*pi             __________
3 - ---- + 5*x - 5*\/ 2*sin(x) 
     4

$$- 5 \sqrt{2 \sin{\left(x \right)}} + \left(5 x + \left(- \frac{5 \pi}{4} + 3\right)\right)$$

3 - 5*pi/4 + 5*x - 5*sqrt(2)*sqrt(sin(x))

Detail solution

Differentiate $- 5 \sqrt{2 \sin{\left(x \right)}} + \left(5 x + \left(- \frac{5 \pi}{4} + 3\right)\right)$ term by term:
1. Differentiate $5 x + \left(- \frac{5 \pi}{4} + 3\right)$ term by term:
  1. The derivative of the constant $- \frac{5 \pi}{4} + 3$ is zero.
  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: $5$
  The result is: $5$
2. 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 $\frac{d}{d x} 2 \sin{\left(x \right)}$ :
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. 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: $- \frac{5 \sqrt{2} \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}}$
The result is: $5 - \frac{5 \sqrt{2} \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}}$

The answer is:

$5 - \frac{5 \sqrt{2} \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}}$

The graph

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Plot the graph f'(x)

The first derivative [src]

        ___       
    5*\/ 2 *cos(x)
5 - --------------
         ________ 
     2*\/ sin(x)

$$5 - \frac{5 \sqrt{2} \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)}}}$$

Simplify

The second derivative [src]

        /                   2    \
    ___ |    ________    cos (x) |
5*\/ 2 *|2*\/ sin(x)  + ---------|
        |                  3/2   |
        \               sin   (x)/
----------------------------------
                4

$$\frac{5 \sqrt{2} \left(2 \sqrt{\sin{\left(x \right)}} + \frac{\cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}}\right)}{4}$$

Simplify

The third derivative [src]

         /         2   \       
     ___ |    3*cos (x)|       
-5*\/ 2 *|2 + ---------|*cos(x)
         |        2    |       
         \     sin (x) /       
-------------------------------
              ________         
          8*\/ sin(x)

$$- \frac{5 \sqrt{2} \left(2 + \frac{3 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}}\right) \cos{\left(x \right)}}{8 \sqrt{\sin{\left(x \right)}}}$$

Simplify

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Derivative of 3-5pi/4+5x-5sqrt2sinx

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The solution