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Derivative of:
Derivative of x/(x^2+1)
Derivative of -sin(x)
Derivative of 2-x
Derivative of sin(x/4)
Identical expressions
asin(one)/x^ two
arc sinus of e of (1) divide by x squared
arc sinus of e of (one) divide by x to the power of two
asin(1)/x2
asin1/x2
asin(1)/x²
asin(1)/x to the power of 2
asin1/x^2
asin(1) divide by x^2
Similar expressions
arcsin(1)/x^2

The derivative of the function/ asin(1)/x^2

Derivative of asin(1)/x^2

The solution

You have entered [src]

asin(1)
-------
    2  
   x

$$\frac{\operatorname{asin}{\left(1 \right)}}{x^{2}}$$

d /asin(1)\
--|-------|
dx|    2  |
  \   x   /

$$\frac{d}{d x} \frac{\operatorname{asin}{\left(1 \right)}}{x^{2}}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x^{2}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  The result of the chain rule is:
  
  $- \frac{2}{x^{3}}$
So, the result is: $- \frac{2 \operatorname{asin}{\left(1 \right)}}{x^{3}}$
Now simplify:

$- \frac{\pi}{x^{3}}$

The answer is:

$- \frac{\pi}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*asin(1)
----------
     3    
    x

$$- \frac{2 \operatorname{asin}{\left(1 \right)}}{x^{3}}$$

Simplify

The second derivative [src]

6*asin(1)
---------
     4   
    x

$$\frac{6 \operatorname{asin}{\left(1 \right)}}{x^{4}}$$

Simplify

The third derivative [src]

-24*asin(1)
-----------
      5    
     x

$$- \frac{24 \operatorname{asin}{\left(1 \right)}}{x^{5}}$$

Simplify

The graph

Derivative of asin(1)/x^2