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find derivative using limit definition?
I just posted this but I put in the wrong function so here it is again
f(x) = √(3x)
find f '(x) using the limit definition f '(x) = lim as h approaches 0 of [f(x+h) - f(x)]/h
1 Answer
- SidLv 61 decade agoFavorite Answer
using first principle of derivatives we get f'(x) as
√(3(x+h)) - √(3x) / h
multiply and divide by √(3(x+h)) + √(3x), we will get
[ (√(3(x+h)) - √(3x) ) * ( √(3(x+h)) + √(3x) ) ] / [ h * (√(3(x+h)) + √(3x) ) ]
= [3(x+h) - 3x] / [ h * (√(3(x+h)) + √(3x) ) ]
= 3h/ [ h * (√(3(x+h)) + √(3x) ) ]
h cancels out and we are left with
3/ [ √(3(x+h)) + √(3x) ]
put limit h->0 in the denominator above and you will get
3 / 2√(3(x)
