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Derivative of:
Derivative of tanh(x)
Derivative of tanx
Derivative of tg2x
Derivative of x^3/(x^2-9)
Graphing y =:
(1/x)+4x^2
Identical expressions
(one /x)+4x^ two
(1 divide by x) plus 4x squared
(one divide by x) plus 4x to the power of two
(1/x)+4x2
1/x+4x2
(1/x)+4x²
(1/x)+4x to the power of 2
1/x+4x^2
(1 divide by x)+4x^2
Similar expressions
(1/x)-4x^2

The derivative of the function/ (1/x)+4x^2

Derivative of (1/x)+4x^2

The solution

You have entered [src]

1      2
- + 4*x 
x

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

1/x + 4*x^2

Detail solution

Differentiate $4 x^{2} + \frac{1}{x}$ term by term:
1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  So, the result is: $8 x$
The result is: $8 x - \frac{1}{x^{2}}$

The answer is:

$8 x - \frac{1}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

$$8 x - \frac{1}{x^{2}}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

-6 
---
  4
 x

$$- \frac{6}{x^{4}}$$

Simplify