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Problem 21 Easy Difficulty

If $ f(x) + x^2[f(x)]^3 = 10 $ and $ f(1) = 2, $ find $ f'(1). $

Answer

$$f^{\prime}(1)=-\frac{16}{13}$$

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Video Transcript

in this problem. We're giving any question anywhere. Um, you like that when X is one, is you going to do them? Whereas to find Derek a function at the same point? So let's like there were two office Given equal ish. We have DF the X. So that is that. Plus for the second German left aside, we're going to use Porter. Cool. So we have two x times off base. You was, uh, X squared times three f squared off pecs terms E l x, The X that is equal zero since wrecked inside is just a constant. So we are ready to know, like values in Were drunk went mental and form one plus two times f o Born Q plus warm times three. That script Warm times F Primal born eyes zero. So we have a pro born WAAS epic. One is to sew to two is eight. We have two times, right, Waas, um, three times for times F from one is zero. So here we see a 13 of primal whore is the night 16 and from the street and see that form a boar is negative 16 over 13