Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^2*x
Derivative of x^sin(x)
Derivative of sqrt(x^2+1)
Derivative of 4/x^2
Integral of d{x}:
6/x^2
Limit of the function:
6/x^2
Identical expressions
six /x^ two
6 divide by x squared
six divide by x to the power of two
6/x2
6/x²
6/x to the power of 2
6 divide by x^2
Similar expressions
6/(x^(2/3))

The derivative of the function/ 6/x^2

Derivative of 6/x^2

The solution

You have entered [src]

6 
--
 2
x

$$\frac{6}{x^{2}}$$

6/x^2

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: $- \frac{12}{x^{3}}$

The answer is:

$- \frac{12}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-12 
----
  3 
 x

$$- \frac{12}{x^{3}}$$

Simplify

The second derivative [src]

36
--
 4
x

$$\frac{36}{x^{4}}$$

Simplify

The third derivative [src]

-144 
-----
   5 
  x

$$- \frac{144}{x^{5}}$$

Simplify

The graph

Derivative of 6/x^2