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5x²-6×(x^-3)+7/x

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Derivative of:
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Derivative of (x^2)/36
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Derivative of e^(sin(x)-2*x^3)
Identical expressions
5x²- six ×(x^- three)+ seven /x
5x² minus 6×(x to the power of minus 3) plus 7 divide by x
5x² minus six ×(x to the power of minus three) plus seven divide by x
5x²-6×(x-3)+7/x
5x²-6×x-3+7/x
5x²-6×x^-3+7/x
5x²-6×(x^-3)+7 divide by x
Similar expressions
5x²-6×(x^-3)-7/x
5x²+6×(x^-3)+7/x
5x²-6×(x^+3)+7/x

The derivative of the function/ 5x²-6×(x^-3)+7/x

Derivative of 5x²-6×(x^-3)+7/x

The solution

You have entered [src]

   2   6    7
5*x  - -- + -
        3   x
       x

$$5 x^{2} + \frac{7}{x} - \frac{6}{x^{3}}$$

d /   2   6    7\
--|5*x  - -- + -|
dx|        3   x|
  \       x     /

$$\frac{d}{d x} \left(5 x^{2} + \frac{7}{x} - \frac{6}{x^{3}}\right)$$

Transform

Detail solution

Differentiate $5 x^{2} + \frac{7}{x} - \frac{6}{x^{3}}$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $10 x$
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. Apply the power rule: $\frac{1}{x^{3}}$ goes to $- \frac{3}{x^{4}}$
    So, the result is: $- \frac{18}{x^{4}}$
  So, the result is: $\frac{18}{x^{4}}$
3. 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: $- \frac{7}{x^{2}}$
The result is: $10 x - \frac{7}{x^{2}} + \frac{18}{x^{4}}$

The answer is:

$10 x - \frac{7}{x^{2}} + \frac{18}{x^{4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  7           18
- -- + 10*x + --
   2           4
  x           x

$$10 x - \frac{7}{x^{2}} + \frac{18}{x^{4}}$$

Simplify

The second derivative [src]

  /    36   7 \
2*|5 - -- + --|
  |     5    3|
  \    x    x /

$$2 \cdot \left(5 + \frac{7}{x^{3}} - \frac{36}{x^{5}}\right)$$

Simplify

The third derivative [src]

  /     60\
6*|-7 + --|
  |      2|
  \     x /
-----------
      4    
     x

$$\frac{6 \left(-7 + \frac{60}{x^{2}}\right)}{x^{4}}$$

Simplify

The graph

Derivative of 5x²-6×(x^-3)+7/x