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Chain Rule

  • Thread starter Shambles
  • Start date
  • #1
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Homework Statement


Find g'(x)
a(x)=x(18-x^2)^1/2

Homework Equations


Answer stated as:
a'(x)=(18-x^2)^1/2 - x^2/(18-x^2)^1/2


The Attempt at a Solution



Having trouble with this solution. The chain rule states that f(x)g(x) = f'(x)g(x)+g'(x)f(x) so the first term in the solution is obviously (18-x^2)^1/2.

Where I run into problems is the second term with the numerator being x^2 when I thought it should only be x. Simplifying the problem into f(x)=(18-x^2)^1/2 the chain rule states it the derivative should be 1/2(18-x^2)(0-2x)=-x/(18-x^2)^1/2. Am I wrong or is the stated solution wrong?
 

Answers and Replies

  • #2
Doc Al
Mentor
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Having trouble with this solution. The chain rule states that f(x)g(x) = f'(x)g(x)+g'(x)f(x) so the first term in the solution is obviously (18-x^2)^1/2.

Where I run into problems is the second term with the numerator being x^2 when I thought it should only be x.
You forgot about f(x) = x, which gives you the second x.
 
  • #3
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Ugh, that is so... dirty. Thanks, that was pretty simple.
 
  • #4
33,079
4,782

Homework Statement


Find g'(x)
a(x)=x(18-x^2)^1/2

Homework Equations


Answer stated as:
a'(x)=(18-x^2)^1/2 - x^2/(18-x^2)^1/2


The Attempt at a Solution



Having trouble with this solution. The chain rule states that f(x)g(x) = f'(x)g(x)+g'(x)f(x) so the first term in the solution is obviously (18-x^2)^1/2.
That's not the chain rule; it's the product rule. The chain rule is used to find the derivative of a composite function, f(g(x)).
Where I run into problems is the second term with the numerator being x^2 when I thought it should only be x. Simplifying the problem into f(x)=(18-x^2)^1/2 the chain rule states it the derivative should be 1/2(18-x^2)(0-2x)=-x/(18-x^2)^1/2. Am I wrong or is the stated solution wrong?
 

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