February 23rd, 2019, 10:58 PM  #1 
Newbie Joined: Feb 2019 From: N/A Posts: 18 Thanks: 0 Math Focus: Calculus  Derivative of (x^21)^2 problem
Is the answer: (2x^22)?

February 24th, 2019, 06:47 AM  #2 
Senior Member Joined: Aug 2012 Posts: 2,204 Thanks: 647 
Chain rule.

February 24th, 2019, 08:54 AM  #3 
Senior Member Joined: Nov 2015 From: United States of America Posts: 195 Thanks: 25 Math Focus: Calculus and Physics 
Use the chain rule to solve this. Our function here, which I will call $h(x) = (x^21)^2$, 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. $\frac{d}{dx} (x^21)^2 = 2(x^21)^1 \frac{d}{dx}(x^21)$ $\Rightarrow 2(x^21)^1 2x$ = 4x(x^21) 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 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,079 Thanks: 845 Math Focus: Wibbly wobbly timeywimey stuff.  

Tags 
calculus, derivative, mikeiketube, problem, x212 
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