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Find the derivative of the function using the definition of derivative. f(x) = 5x

Sagot :

The derivative is f'(x) = 5.

The limit definition of the derivative tells us that the derivative of a function is f is

f' (x) = [tex]\lim_{h \to \0} 0[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]

For this, f(x) = 5x and f(x + h) = 5(x + h)

So:

f'(x) = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5(x+h)-5x}{h}[/tex]

        = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5x+5h-5x}{h}[/tex]

       = [tex]\lim_{h \to \}0[/tex] [tex]\frac{5h}{h}[/tex]

       = [tex]\lim_{h \to \}0[/tex] 5

       = 5

So, when f(x) = 5x , we see that its derivative is f'(x) = 5.

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