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Derivative of:
Derivative of 9/x
Derivative of x^-5
Derivative of x^2*e^x
Derivative of x^2*cos(x)
Identical expressions
pi^ two *a*cos(pi*x/(two *l))/((four *l^ two))
Pi squared multiply by a multiply by co sinus of e of ( Pi multiply by x divide by (2 multiply by l)) divide by ((4 multiply by l squared ))
Pi to the power of two multiply by a multiply by co sinus of e of ( Pi multiply by x divide by (two multiply by l)) divide by ((four multiply by l to the power of two))
pi2*a*cos(pi*x/(2*l))/((4*l2))
pi2*a*cospi*x/2*l/4*l2
pi²*a*cos(pi*x/(2*l))/((4*l²))
pi to the power of 2*a*cos(pi*x/(2*l))/((4*l to the power of 2))
pi^2acos(pix/(2l))/((4l^2))
pi2acos(pix/(2l))/((4l2))
pi2acospix/2l/4l2
pi^2acospix/2l/4l^2
pi^2*a*cos(pi*x divide by (2*l)) divide by ((4*l^2))

Derivative of pi^2acos(pix/(2l))/((4*l^2))

You have entered [src]

  2      /pi*x\
pi *a*cos|----|
         \2*l /
---------------
         2     
      4*l

$$\frac{\pi^{2} a \cos{\left(\frac{\pi x}{2 l} \right)}}{4 l^{2}}$$

((pi^2*a)*cos((pi*x)/((2*l))))/((4*l^2))

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \frac{\pi x}{2 l}$ .
  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 $\frac{\partial}{\partial x} \frac{\pi x}{2 l}$ :
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      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: $\pi$
      So, the result is: $\pi \frac{1}{2 l}$
    The result of the chain rule is:
    
    $- \frac{\pi \sin{\left(\frac{\pi x}{2 l} \right)}}{2 l}$
  So, the result is: $- \frac{\pi^{3} a \sin{\left(\frac{\pi x}{2 l} \right)}}{2 l}$
So, the result is: $- \frac{\pi^{3} a \frac{1}{4 l^{2}} \sin{\left(\frac{\pi x}{2 l} \right)}}{2 l}$
Now simplify:

$- \frac{\pi^{3} a \sin{\left(\frac{\pi x}{2 l} \right)}}{8 l^{3}}$

The answer is:

$- \frac{\pi^{3} a \sin{\left(\frac{\pi x}{2 l} \right)}}{8 l^{3}}$

The first derivative [src]

     3  1      /pi*x\ 
-a*pi *----*sin|----| 
          2    \2*l / 
       4*l            
----------------------
         2*l

$$- \frac{\pi^{3} a \frac{1}{4 l^{2}} \sin{\left(\frac{\pi x}{2 l} \right)}}{2 l}$$

Simplify

The second derivative [src]

     4    /pi*x\ 
-a*pi *cos|----| 
          \2*l / 
-----------------
          4      
      16*l

$$- \frac{\pi^{4} a \cos{\left(\frac{\pi x}{2 l} \right)}}{16 l^{4}}$$

Simplify

The third derivative [src]

    5    /pi*x\
a*pi *sin|----|
         \2*l /
---------------
         5     
     32*l

$$\frac{\pi^{5} a \sin{\left(\frac{\pi x}{2 l} \right)}}{32 l^{5}}$$

Simplify

Derivative of pi^2*a*cos(pi*x/(2*l))/((4*l^2))