Question

evaluate the derivative of s(t) = √(t^2 + 2t + 8) at the point (2,4)

Answer 1

For this derivative, you can use the special case of the square root function: d/dx(sqrt (u)=u prime/sqrt (u)

Answer 2

derivative of
\[\sqrt{g(x)}=\frac{g'(x)}{2\sqrt{g(x)}}\]

Answer 3

what @L.T. said, but don't forget the 2 in the denominator

Answer 4

ugh im sorry but i dont get it :\

Answer 5

Do you know what the chain rule is?? it's slightly longer than the shortcut shown above, but will still work.

Answer 6

\[(t^2+2t+8)^{\frac{ 1 }{ 2 }}\]

Answer 7

\[\frac{ 1 }{ 2 }(t^2+2t+8)^{-\frac{ 1 }{ 2 }}(2t+2)\]

Answer 8

your \(g(t)=t^2+2t+8\) and \(g'(t)=2t+2\) so your derivative if
\[\frac{2t+2}{2\sqrt{t^2+2t+8}}\]

Answer 9

@ksandoval Your thoughts??

Answer 10

@ChmE is using the power rule and the chain rule, and it is a good explanation, but if you have to do more than one of these it is good to remember that the derivative of root x is one over two root x,
and the derivative of root something is the derivative of something, over two root something

Answer 11

yes i know what the chain rule is. and okay i get that but know what do i do with the point that im given?

Answer 12

don't forget that you are going to have to evaluate the derivative, and you cannot evaluate
\[\frac{1}{2}(t^2+2t+8)^{-\frac{1}{2}}(2t+2)\] without first writing it as
\[\frac{2t+2}{2\sqrt{t^2+2t+8}}\]

Answer 13

yes, replace \(x\) by 2

Answer 14

It is asking for the slope at that point. What @satellite73 said.in this case t by 2

Answer 15

thanks to both of you guys!