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Derivative of:
Derivative of cos(x/3)
Derivative of √x
Derivative of x|x|
Derivative of y=3x-2
Identical expressions
x^ five +3x^(- two)+4x
x to the power of 5 plus 3x to the power of ( minus 2) plus 4x
x to the power of five plus 3x to the power of ( minus two) plus 4x
x5+3x(-2)+4x
x5+3x-2+4x
x⁵+3x^(-2)+4x
x^5+3x^-2+4x
Similar expressions
x^5-3x^(-2)+4x
x^5+3x^(2)+4x
x^5+3x^(-2)-4x

The derivative of the function/ x^5+3x^(-2)+4x

Derivative of x^5+3x^(-2)+4x

The solution

You have entered [src]

 5   3       
x  + -- + 4*x
      2      
     x

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

x^5 + 3/x^2 + 4*x

Detail solution

Differentiate $4 x + \left(x^{5} + \frac{3}{x^{2}}\right)$ term by term:
1. Differentiate $x^{5} + \frac{3}{x^{2}}$ term by term:
  1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $\frac{1}{x^{2}}$ goes to $- \frac{2}{x^{3}}$
    So, the result is: $- \frac{6}{x^{3}}$
  The result is: $5 x^{4} - \frac{6}{x^{3}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $4$
The result is: $5 x^{4} + 4 - \frac{6}{x^{3}}$

The answer is:

$5 x^{4} + 4 - \frac{6}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    6       4
4 - -- + 5*x 
     3       
    x

$$5 x^{4} + 4 - \frac{6}{x^{3}}$$

Simplify

The second derivative [src]

  /9        3\
2*|-- + 10*x |
  | 4        |
  \x         /

$$2 \left(10 x^{3} + \frac{9}{x^{4}}\right)$$

Simplify

The third derivative [src]

   /  6       2\
12*|- -- + 5*x |
   |   5       |
   \  x        /

$$12 \left(5 x^{2} - \frac{6}{x^{5}}\right)$$

Simplify