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find the derivative of f(x)=x^2 + x 3 using the definition of the derivative
 one year ago
 one year ago
find the derivative of f(x)=x^2 + x 3 using the definition of the derivative
 one year ago
 one year ago

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CallistoBest ResponseYou've already chosen the best response.3
\[f'(x)\]\[=\lim_{h \rightarrow 0}\frac{f(x+h)  f(x)}{h}\]\[=\lim_{h \rightarrow 0}\frac{[(x+h)^2 + (x+h) 3] (x^2 + x 3)}{h}\]Can you simplify the fraction first?
 one year ago

bigcatBest ResponseYou've already chosen the best response.0
I used x^2 + 2(x)(h) + h^2 + x +h 3 x^2 x +3 = 2x + x ??
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
x^2 + 2(x)(h) + h^2 + x +h 3 x^2 x +3 < correct for denominator. But it's not equal to 2x + x... \[x^2 + 2(x)(h) + h^2 + x +h 3 x^2 x +3\]Group the like terms together: \[x^2 x^2 + x x 3 +3+ h^2+ 2(x)(h)+h\] Now, can you simplify the above expression
 one year ago

bigcatBest ResponseYou've already chosen the best response.0
basically factor out the h and H(h+2x+1) divided by the h on denominator and = h + 2x + 1?
 one year ago

CallistoBest ResponseYou've already chosen the best response.3
And you got: \[\lim_{h \rightarrow 0} (h+2x+1)\]Can you evaluate the limit?
 one year ago

bigcatBest ResponseYou've already chosen the best response.0
Would be 2x + 1 ??? Because h is going to 0
 one year ago

bigcatBest ResponseYou've already chosen the best response.0
Holy Cow! It came together finally!! Thank you very much for your help! I would have been stuck!!!
 one year ago
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