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f(x) = x² + 5
f(x + h) - f(x)
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.h
f (x + h) = (x + h)² + 5(x + h)
f (x + h) = (x + h)(x + h) + 5(x + h)
f (x + h) = x² + 2hx + h² + 5x + 5h
f(x + h) - f(x)
_________
.h
x² + 2hx + h² + 5x + 5h - (x² + 5x)
_________________________
. h
x² + 2hx + h² + 5x + 5h - x² - 5x
________________________
.h
2hx + h² + 5h
__________
.h
h(2x + h + 5)
_________
. h
f = 2x + h + 5