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Derivative of:
Derivative of -2x/(1+x^2)^2
Derivative of f(x)=x^3
Derivative of 5/x^3
Derivative of 3*sin(x)^(2)
Identical expressions
(three /x)-2sqrt(x)+ seven
(3 divide by x) minus 2 square root of (x) plus 7
(three divide by x) minus 2 square root of (x) plus seven
(3/x)-2√(x)+7
3/x-2sqrtx+7
(3 divide by x)-2sqrt(x)+7
Similar expressions
(3/x)+2sqrt(x)+7
(3/x)-2sqrt(x)-7

The derivative of the function/ (3/x)-2sqrt(x)+7

Derivative of (3/x)-2sqrt(x)+7

The solution

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3       ___    
- - 2*\/ x  + 7
x

$$\left(- 2 \sqrt{x} + \frac{3}{x}\right) + 7$$

3/x - 2*sqrt(x) + 7

Detail solution

Differentiate $\left(- 2 \sqrt{x} + \frac{3}{x}\right) + 7$ term by term:
1. Differentiate $- 2 \sqrt{x} + \frac{3}{x}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
    So, the result is: $- \frac{3}{x^{2}}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
    So, the result is: $- \frac{1}{\sqrt{x}}$
  The result is: $- \frac{3}{x^{2}} - \frac{1}{\sqrt{x}}$
2. The derivative of the constant $7$ is zero.
The result is: $- \frac{3}{x^{2}} - \frac{1}{\sqrt{x}}$

The answer is:

$- \frac{3}{x^{2}} - \frac{1}{\sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    1     3 
- ----- - --
    ___    2
  \/ x    x

$$- \frac{3}{x^{2}} - \frac{1}{\sqrt{x}}$$

Simplify

The second derivative [src]

  1      6 
------ + --
   3/2    3
2*x      x

$$\frac{6}{x^{3}} + \frac{1}{2 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

   /6      1   \
-3*|-- + ------|
   | 4      5/2|
   \x    4*x   /

$$- 3 \left(\frac{6}{x^{4}} + \frac{1}{4 x^{\frac{5}{2}}}\right)$$

Simplify