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The derivative of the function/ 5x^2-4x+9

Derivative of 5x^2-4x+9

The solution

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   2          
5*x  - 4*x + 9

$$5 x^{2} - 4 x + 9$$

d /   2          \
--\5*x  - 4*x + 9/
dx

$$\frac{d}{d x} \left(5 x^{2} - 4 x + 9\right)$$

Transform

Detail solution

Differentiate $5 x^{2} - 4 x + 9$ 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: $10 x$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. 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: $4$
  So, the result is: $-4$
3. The derivative of the constant $9$ is zero.
The result is: $10 x - 4$

The answer is:

$10 x - 4$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-4 + 10*x

$$10 x - 4$$

Simplify

The second derivative [src]

$$10$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of 5x^2-4x+9