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Derivative of:
Derivative of asin(x)
Derivative of cos(x^3)
Derivative of (cos(x))^3
Derivative of 1/tan(x)
Identical expressions
(x^ two +x)/ two
(x squared plus x) divide by 2
(x to the power of two plus x) divide by two
(x2+x)/2
x2+x/2
(x²+x)/2
(x to the power of 2+x)/2
x^2+x/2
(x^2+x) divide by 2
Similar expressions
(x^2-x)/2

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

Derivative of (x^2+x)/2

The solution

You have entered [src]

 2    
x  + x
------
  2

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

(x^2 + x)/2

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1/2 + x

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

Simplify

The second derivative [src]

$$1$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of (x^2+x)/2