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Find the derivative with and without using the chain rule. f(x) = (x^2 + 1)^3
 one year ago
 one year ago
Find the derivative with and without using the chain rule. f(x) = (x^2 + 1)^3
 one year ago
 one year ago

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ingenuusBest ResponseYou've already chosen the best response.0
\[f(x)=(x^2+1)^3=(x^2+1)(x^2+1)(x^2+1)\] \[f'(x)=6x(x^2+1)^2\]
 one year ago

ingenuusBest ResponseYou've already chosen the best response.0
used only product rule
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
is that using the chain rule?
 one year ago

ingenuusBest ResponseYou've already chosen the best response.0
no. i said i only used product rule.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
One, do you understand how to find the derivative `with` using chain rule? You would just take the derivative as is.
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
okay i'll try doing with the chain rule
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
okay can i post it here and correct me if i i mistake somewhere
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
\[d/dx ((x^2 + 1)^3) = 3(x^2 + 1)^2 d/dx(x^2 + 1) = 3(d/dx(x^2)(x^2  1)^2 = 3(2x)(x^2 = 1)^2 = 6x(x^2 + 1)^2 \]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
I'm not quite sure why it changed from x^2+1 to x^21. Was that a typo?
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
i see that it didn't show up all of it but here is the last part 3(2x)(x^2 + 1)^2 = 6x(x^2 + 1)^2
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large f'(x)=3(x^2+1)^2\frac{d}{dx}(x^2+1)\]\[\large f'(x)=3(x^2+1)^2(2x) \qquad \qquad f'(x)=6x(x^2+1)^2\] Ok yah looks good :)
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
`without` chain rule is going to be a little tricky. They want you multiply out your binomial :O oh boy.
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
ohh so the one @ingenuus showed is nto by without chain rule?
 one year ago

onegirlBest ResponseYou've already chosen the best response.0
the one ingenuus showed its using the product rule
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
That's another method for doing it without chain rule. Which involved the product rule with `3 terms`. Which is a little bit tricky if you've never seen it before. Product rule with 2 terms is probably what you're used to seeing. I was referring to a different method, multiplying out all the brackets as Wio showed you the last time you posted this. :D
 one year ago
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