Question #a0dee

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Answer 1 · 2016-09-04T16:33:12

#10 x#

We have: #f(x) = 5 x^(2) - 3#

#=> f'(x) = lim_(h -> 0) (f(x + h) - f(x)) / (h)#

#=> f'(x) = lim_(h -> 0) ((5 (x + h)^(2) - 3) - (5 x^(2) - 3)) / (h)#

#=> f'(x) = lim_(h -> 0) (5 (x^(2) + 2 h x + h^(2)) - 3 - 5 x^(2) + 3) / (h)#

#=> f'(x) = lim_(h -> 0) (5 x^(2) + 10 h x + 5 h^(2) - 5 x^(2)) / (h)#

#=> f'(x) = lim_(h -> 0) (10 h x + 5 h^(2)) / (h)#

#=> f'(x) = lim_(h -> 0) 10 x + h#

#=> f'(x) = 10 x#