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Derivative of:
Derivative of x^4*e^x
Derivative of f(x)=2x+3
Derivative of 2/(x+1)
Derivative of (1/x)^x
Integral of d{x}:
1/sin(2*x)
Graphing y =:
1/sin(2*x)
Limit of the function:
1/sin(2*x)
Identical expressions
one /sin(two *x)
1 divide by sinus of (2 multiply by x)
one divide by sinus of (two multiply by x)
1/sin(2x)
1/sin2x
1 divide by sin(2*x)
Similar expressions
tan(2x^2-1)/sin(2x^2-1)
y'=(1/sin^2x)-cosx+x^2
(arctg(2x+1))/(sin^2(x))
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The derivative of the function/ 1/sin(2*x)

Derivative of 1/sin(2*x)

The solution

You have entered [src]

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

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

1/sin(2*x)

Detail solution

Let $u = \sin{\left(2 x \right)}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(2 x \right)}$ :
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 $\frac{d}{d x} 2 x$ :
  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: $2$
  The result of the chain rule is:
  
  $2 \cos{\left(2 x \right)}$
The result of the chain rule is:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*cos(2*x)
-----------
    2      
 sin (2*x)

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

Simplify

The second derivative [src]

  /         2     \
  |    2*cos (2*x)|
4*|1 + -----------|
  |        2      |
  \     sin (2*x) /
-------------------
      sin(2*x)

$$\frac{4 \left(1 + \frac{2 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right)}{\sin{\left(2 x \right)}}$$

Simplify

The third derivative [src]

   /         2     \         
   |    6*cos (2*x)|         
-8*|5 + -----------|*cos(2*x)
   |        2      |         
   \     sin (2*x) /         
-----------------------------
             2               
          sin (2*x)

$$- \frac{8 \left(5 + \frac{6 \cos^{2}{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}\right) \cos{\left(2 x \right)}}{\sin^{2}{\left(2 x \right)}}$$

Simplify

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Identical expressions

Similar expressions

Derivative of 1/sin(2*x)

The graph:

Piecewise:

The solution