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Derivative of:
Derivative of (x+2)/(x^2-9)
Derivative of (x+1)/x
Derivative of x^2+5
Derivative of (x^2+36)/x
Identical expressions
lnsqrt(sin2x/ one -sin2x)
ln square root of ( sinus of 2x divide by 1 minus sinus of 2x)
ln square root of ( sinus of 2x divide by one minus sinus of 2x)
ln√(sin2x/1-sin2x)
lnsqrtsin2x/1-sin2x
lnsqrt(sin2x divide by 1-sin2x)
Similar expressions
lnsqrt(sin2x/1+sin2x)

The derivative of the function/ lnsqrt(sin2x/1-sin2x)

Derivative of lnsqrt(sin2x/1-sin2x)

The solution

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   /    _____________________\
   |   / sin(2*x)            |
log|  /  -------- - sin(2*x) |
   \\/      1                /

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

log(sqrt(sin(2*x)/1 - sin(2*x)))

Detail solution

Let $u = \sqrt{- \sin{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{1}}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{- \sin{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{1}}$ :
1. Let $u = - \sin{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{1}$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- \sin{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{1}\right)$ :
  1. Differentiate $- \sin{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{1}$ term by term:
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Let $u = 2 x$ .
      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 $\frac{d}{d x} 2 x$ :
        
        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:
        
        $2 \cos{\left(2 x \right)}$
      So, the result is: $2 \cos{\left(2 x \right)}$
    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 sine is cosine:
        
        $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
        
        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:
        
        $2 \cos{\left(2 x \right)}$
      So, the result is: $- 2 \cos{\left(2 x \right)}$
    The result is: $0$
  The result of the chain rule is:
  
  $0$
The result of the chain rule is:

$0$

The answer is:

$0$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

$$0$$

Simplify

The second derivative [src]

$$0$$

Simplify

The third derivative [src]

$$0$$

Simplify

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Derivative of lnsqrt(sin2x/1-sin2x)

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The solution