Let r(x)=F(g(h))), where h(1)=2, g(2)=5, h'(1)=4, g'(2)=4, and f'(5)=6. Find r'(1).
This is a really unusual question.
Let r(x)=F(g(h))),
where h(1)=2, g(2)=5, h'(1)=4, g'(2)=4, and f'(5)=6. [I will assume tht f'(5) is really F'(5)]
Find r'(1).
\(r(x)=F(g(h))\\ r(x)=F(g(h(x)))\\ r'(x)=F'(g(h(x)))\\ r'(1)=F'(g(h(1)))\\ r'(1)=F'(g(2))\\ r'(1)=F'(5)\\ r'(1)=6\\ \)
Hi Alan,
I have been trying to work out what you have said.
I understand your example of course but I do not understand why that means that this is the only answer. How can you take just one example and say the answer is always going to be the same.??
Let r(x)=F(g(h))), where h(1)=2, g(2)=5, h'(1)=4, g'(2)=4, and f'(5)=6. Find r'(1).
I think this is right.
\(\begin{align} \frac{dr}{dx}&=\frac{df}{dg} \cdot \frac{dg}{dh}\cdot \frac{dh}{dx}\\ \end{align} \)
I'm told that when x=1 dh/dx =2 but I don't know from the info given what the other two derivatives are. How can I use all that other information without resorting to a specific example ???