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

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Callisto
 2 years ago
Best 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?

bigcat
 2 years ago
Best ResponseYou've already chosen the best response.0I used x^2 + 2(x)(h) + h^2 + x +h 3 x^2 x +3 = 2x + x ??

Callisto
 2 years ago
Best ResponseYou've already chosen the best response.3x^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

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

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

bigcat
 2 years ago
Best ResponseYou've already chosen the best response.0Would be 2x + 1 ??? Because h is going to 0

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