Respuesta :

Step-by-step explanation:

We got

[tex] \frac{f(x + h) - f(x)}{h} [/tex]

The function here is

9x^2 so we got now

[tex] \frac{9(x + h) {}^{2} - 9 {x}^{2} }{h} [/tex]

[tex] \frac{9( {x}^{2} + 2hx + {h}^{2} - 9 {x}^{2} }{h} [/tex]

[tex] \frac{9 {x}^{2} + 18hx + 9 {h}^{2} - 9 {x}^{2} }{h} [/tex]

Cancel out terms.

[tex] \frac{18hx + 9h {}^{2} }{h} [/tex]

If we direct subsitue we get

[tex] \frac{0}{0} [/tex]

which is intermidate form in calculus so now, let try to find another way to evaluate this, we can factor out 9h

[tex] \frac{9h(2x + h}{h} [/tex]

Cancel out h

[tex]9(2x + h)[/tex]

Subsitue 0 for h.

[tex]9(2x + 0)[/tex]

[tex]9(2x)[/tex]

[tex]18x[/tex]

The answer here is 18x.

Congrats. We just found the derivative of a function.

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