Posted by Lauren on Wednesday, April 1, 2009 at 6:40am.
I finished this problem but I wanted some feedback because I don't know if it's entirely correct.
Suppose that functions f and g and their derivatives with respect to x have the following values at x=2.
Find d/dx of f(g(x)) at x=2.
I know the chain rule is this:
f'(g(x)) * g'(x)
So you would write the derivative of the outer function, keeping the inner function (g(x)) as the 'x' value. But in this case, the derivative of the outer function is a number.... I wasn't sure how to approach this problem. How do I figure in the g(x)?
This is the answer (and work) that I got:
f'(g(x)) * g'(x)
1/3 * -3 = -1
Where 1/3 is f'(x) and -3 is g'(x). But I feel like this is incorrect, because I didn't input the value of g(x).
Does anyone know if what I did was right, or how to correct it if it was wrong? I wasn't given an equation for f(x) or g(x) so I assumed we were supposed to rely on the numbers given. Do I need to multiply f'(x) and g(x) to get 2/3?
- Calculus - Damon, Wednesday, April 1, 2009 at 9:00am
g(2) = 2
f'(2) = 1/3
f'(g(2)) = 2/3
g'(2) = -3
so I get
(2/3)(-3) = -2
- Calculus - Lauren, Wednesday, April 1, 2009 at 10:01am
Thank you! That makes more sense... because you would say f' of g of x.... so 1/3 of 2 = 2/3. That makes sense!
Answer this Question
Geometry Part 2 - At a track meet,50 people ran the 100- meter dash.2 people ...
pre alegbra - can you help me figure this question out? In a race with five ...
English - Posted by rfvv on Sunday, May 2, 2010 at 10:33pm. 1. Are you finished ...
math - rocio finished 21 pages of a book in 3 days. monday she finished half of ...
7th grade math - After 1 hour,Jon had finished 5/9 of a long-distance race, and ...
calculus - Okay, so I have this problem... this was the original: (t^2-1?t^2+1...
English - Chosse the simple predicate in the following sentence. The men ...
Algebra 1 - 4. Two consultants were hired by a company. The total consultant ...
Calculus - What is the simplest solution to the Brachistochrone problem and the ...
math - Nina finished 4/8 of her homework before dinner. Ed finished 7/8 of his ...