Question

CALCULUS PROBLEM PLEASE HELP
If f(2)=3, f'(2)=-4, g(2)=-2, and g'(2)=6, find h'(2) if h(x)=f(x)g(x) I have the answer which is 26 can someone help me with the solution? PLEASE

Answer 1

\[h(x) = f(x)\cdot g(x)\]\[d\left[h(x)=f(x)\cdot g(x)\right] \implies h'(x) = f'(x) \cdot g(x) +g'(x)\cdot f(x)\]

Answer 2

Now would you be able to plug in your values accordingly?

Answer 3

\[h'(2) = f'(2)\cdot g(2) +g'(2)\cdot f(2)\]Just input your values and solve for h'(2) :)

Answer 4

thank you very much!

Answer 5

no problem :D

Answer 6

how about h(x)=square root of g(x) ? can you help me with this one

Answer 7

finding the derivative?

Answer 8

its part of the previous one like substitute the numbers in it

Answer 9

Ah ok.

Answer 10

\[h(x) = \sqrt{g(x)}\]\[h(x) = g(x)^{1/2}\]\[d\left[h(x) = g(x)^{1/2}\right] \implies h'(x) = \frac{1}{2\sqrt{g(x)}}\]

Answer 11

thanks really appreciate it this is the last one i promise lol how about h(x)=(f(x))^3 the answer should be -108

Answer 12

Haha, no problem :) Feeling a little sleepy as a matter of fact.

Answer 13

\[h(x) = (f(x))^2\]\[d\left[h(x) = (f(x))^2\right]\]\[h'(x) = 2(f(x))^{2-1}\]

Answer 14

Good luck! :) i am off