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 February 23rd, 2019, 10:58 PM #1 Newbie   Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus Derivative of (x^2-1)^2 problem Is the answer: (2x^2-2)? February 24th, 2019, 06:47 AM #2 Senior Member   Joined: Aug 2012 Posts: 2,393 Thanks: 749 Chain rule. February 24th, 2019, 08:54 AM #3 Senior Member   Joined: Nov 2015 From: United States of America Posts: 198 Thanks: 25 Math Focus: Calculus and Physics Use the chain rule to solve this. Our function here, which I will call $h(x) = (x^2-1)^2$, is a composition of two functions. You have the inner function which I will define as a $g(x) = x^2 - 1$ and the outer function which takes this inner function g(x) and raises it two the power of two ($(g(x)^2$). Which is a function of itself that I will define as $f(x)$. The chain rule states $\frac{d}{dx}h(x) = f'(g(x))g'(x)$ In a simplified analogy, you can think about this as multiplying the derivative of the "outside" (keeping the "inside" the same) by the derivative of the inside. Here we go. $\frac{d}{dx} (x^2-1)^2 = 2(x^2-1)^1 \frac{d}{dx}(x^2-1)$ $\Rightarrow 2(x^2-1)^1 2x$ = 4x(x^2-1) Notice in the first step, all I did was use the power rule on the exponent on the outside of the parentheses and kept the stuff inside the parentheses constant. Then I multiplied this result by the derivative of the stuff on the inside of the parentheses. Hope this is clear. February 24th, 2019, 09:32 AM   #4
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Quote:
 Originally Posted by MikeAndIke Is the answer: (2x^2-2)?
The chain rule is good here. But you can simply expand it:
$\displaystyle (x^2 - 1)^2 = (x^2)^2 + 2 \cdot (x^2) \cdot (-1) + (-1)^2 = x^4 - 2x^2 + 1$.

Now take your derivative.

-Dan Tags calculus, derivative, mikeiketube, problem, x212 Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post lackofimagination Calculus 1 July 6th, 2014 08:05 PM bongantedd Calculus 2 May 6th, 2014 08:30 AM KMT Calculus 1 September 25th, 2011 06:55 PM azelio Algebra 2 October 17th, 2010 05:24 PM StevenMx Calculus 6 February 4th, 2009 07:14 AM

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