is the result different if it is found by definition or by the shortcut method?
2007-10-08 18:30:00 · 2 answers · asked by student 2 in Science & Mathematics ➔ Mathematics
same either way....but the definition is harder.........
for 7.5 (x^2) - x + 4.2
then derivative is... 7.5 ( 2x) - 1, or 15x -1
by def'n....
lim h -->0 [ ( 7.5( x + h )^2 - ( x + h) + 4.2 ) - ( 7.5x^2 - x + 4.2 ) ] / h, ... is 0 / 0, so simplify and cancel...
lim h -->0 [ ( 7.5 x^2 + 15xh + 7.5 h^2 ) - ( x + h) + 4.2 ) - ( 7.5x^2 - x + 4.2 ) ] / h
lim h -->0 [ 15xh + 7.5h^2 - h ] / h =
lim h -->0 [ 15x + 7.5 h - 1 ] = 15x - 1
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if you meant [ 7.5x]^2 - x + 4.2, then the deriv = 2 *7.5x * 7.5 -1 = 112.5x -1, and the "long way", by definition, is similar....
2007-10-08 18:33:31 · answer #1 · answered by Mathguy 5 · 0⤊ 0⤋
dy/dx = 15x - 1
Result will be the same.
2007-10-09 06:24:17 · answer #2 · answered by Como 7 · 0⤊ 0⤋