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Derivative of:
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Graphing y =:
-x^2+2*x+3
Factor polynomial:
-x^2+2*x+3
Factor squared:
-x^2+2*x+3
Identical expressions
-x^ two + two *x+ three
minus x squared plus 2 multiply by x plus 3
minus x to the power of two plus two multiply by x plus three
-x2+2*x+3
-x²+2*x+3
-x to the power of 2+2*x+3
-x^2+2x+3
-x2+2x+3
Similar expressions
-x^2+2*x-3
x^2+2*x+3
-x^2-2*x+3

The derivative of the function/ -x^2+2*x+3

Derivative of -x^2+2*x+3

The solution

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   2          
- x  + 2*x + 3

$$\left(- x^{2} + 2 x\right) + 3$$

-x^2 + 2*x + 3

Detail solution

Differentiate $\left(- x^{2} + 2 x\right) + 3$ term by term:
1. Differentiate $- x^{2} + 2 x$ 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: $- 2 x$
  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: $2$
  The result is: $2 - 2 x$
2. The derivative of the constant $3$ is zero.
The result is: $2 - 2 x$

The answer is:

$2 - 2 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2 - 2*x

$$2 - 2 x$$

Simplify

The second derivative [src]

-2

$$-2$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of -x^2+2*x+3