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Similar expressions
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The derivative of the function/ 4/sqrx+3/x-2e^x

Derivative of 4/sqrx+3/x-2e^x

The solution

You have entered [src]

4    3      x
-- + - - 2*E 
 2   x       
x

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

4/x^2 + 3/x - 2*exp(x)

Detail solution

Differentiate $- 2 e^{x} + \left(\frac{4}{x^{2}} + \frac{3}{x}\right)$ term by term:
1. Differentiate $\frac{4}{x^{2}} + \frac{3}{x}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. 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: $- \frac{8}{x^{3}}$
  2. 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: $- \frac{3}{x^{2}}$
  The result is: $- \frac{3}{x^{2}} - \frac{8}{x^{3}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $e^{x}$ is itself.
  So, the result is: $- 2 e^{x}$
The result is: $- 2 e^{x} - \frac{3}{x^{2}} - \frac{8}{x^{3}}$

The answer is:

$- 2 e^{x} - \frac{3}{x^{2}} - \frac{8}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  8    3       x
- -- - -- - 2*e 
   3    2       
  x    x

$$- 2 e^{x} - \frac{3}{x^{2}} - \frac{8}{x^{3}}$$

Simplify

The second derivative [src]

  /   x   3    12\
2*|- e  + -- + --|
  |        3    4|
  \       x    x /

$$2 \left(- e^{x} + \frac{3}{x^{3}} + \frac{12}{x^{4}}\right)$$

Simplify

The third derivative [src]

   /9    48    x\
-2*|-- + -- + e |
   | 4    5     |
   \x    x      /

$$- 2 \left(e^{x} + \frac{9}{x^{4}} + \frac{48}{x^{5}}\right)$$

Simplify