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Derivative of:
Derivative of e^x^2
Derivative of sin(x)^2
Derivative of 225/x+x+6
Derivative of log(4*x+5)
Identical expressions
x^ two +4x+(six /x)
x squared plus 4x plus (6 divide by x)
x to the power of two plus 4x plus (six divide by x)
x2+4x+(6/x)
x2+4x+6/x
x²+4x+(6/x)
x to the power of 2+4x+(6/x)
x^2+4x+6/x
x^2+4x+(6 divide by x)
Similar expressions
x^2+4x-(6/x)
x^2-4x+(6/x)

The derivative of the function/ x^2+4x+(6/x)

Derivative of x^2+4x+(6/x)

The solution

You have entered [src]

 2         6
x  + 4*x + -
           x

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

x^2 + 4*x + 6/x

Detail solution

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

The answer is:

$2 x + 4 - \frac{6}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    6       
4 - -- + 2*x
     2      
    x

$$2 x + 4 - \frac{6}{x^{2}}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

-36 
----
  4 
 x

$$- \frac{36}{x^{4}}$$

Simplify