SOLUTION: if {{{y=4x^3}}} find dy/dx using first principle .

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Question 1110358: if y=4x%5E3 find dy/dx using first principle .
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
+dy%2Fdx+=+lim%28h-%3E0%2C++%28%284%28x%2Bh%29%5E3+-+4x%5E3%29%29%2Fh%29%29+
= +lim%28h-%3E0%2C+++%28%284x%5E3%2B12hx%5E2+%2B+12h%5E2x+%2B+4h%5E3+-+4x%5E3%29%2Fh%29+%29+
The +4x%5E3+-+4x%5E3+ can be crossed out:
= ++lim%28h-%3E0%2C+++%28%2812hx%5E2+%2B+12h%5E2x+%2B+4h%5E3+%29%2Fh%29%29+++
Divide the numerator through by the h from the denominator:
= ++lim%28h-%3E0%2C++%2812x%5E2+%2B+12hx+%2B+4h%5E2%29%29+
= +12x%5E2+