Mister Exam

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The derivative of the function/ x^2-x+1

Derivative of x^2-x+1

The solution

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 2        
x  - x + 1

$$\left(x^{2} - x\right) + 1$$

x^2 - x + 1

Detail solution

Differentiate $\left(x^{2} - x\right) + 1$ term by term:
1. Differentiate $x^{2} - x$ 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: $-1$
  The result is: $2 x - 1$
2. The derivative of the constant $1$ is zero.
The result is: $2 x - 1$

The answer is:

$2 x - 1$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-1 + 2*x

$$2 x - 1$$

Simplify

The second derivative [src]

$$2$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of x^2-x+1