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Derivative of:
Derivative of (sin(x))^2
Derivative of x-1
Derivative of sin(x)+cos(x)
Derivative of asin(x)
Identical expressions
one / four - four /x^ two
1 divide by 4 minus 4 divide by x squared
one divide by four minus four divide by x to the power of two
1/4-4/x2
1/4-4/x²
1/4-4/x to the power of 2
1 divide by 4-4 divide by x^2
Similar expressions
1/4+4/x^2

The derivative of the function/ 1/4-4/x^2

Derivative of 1/4-4/x^2

The solution

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$$\frac{1}{4} - \frac{4}{x^{2}}$$

d /1   4 \
--|- - --|
dx|4    2|
  \    x /

$$\frac{d}{d x} \left(\frac{1}{4} - \frac{4}{x^{2}}\right)$$

Transform

Detail solution

Differentiate $\frac{1}{4} - \frac{4}{x^{2}}$ term by term:
1. The derivative of the constant $\frac{1}{4}$ is zero.
2. 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 $u = x^{2}$ .
    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: $- \frac{8}{x^{3}}$
  So, the result is: $\frac{8}{x^{3}}$
The result is: $\frac{8}{x^{3}}$

The answer is:

$\frac{8}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

8 
--
 3
x

$$\frac{8}{x^{3}}$$

Simplify

The second derivative [src]

-24 
----
  4 
 x

$$- \frac{24}{x^{4}}$$

Simplify

The third derivative [src]

96
--
 5
x

$$\frac{96}{x^{5}}$$

Simplify

The graph

Derivative of 1/4-4/x^2