Question

find the derivative of sqrt((f(x)^2+g(x)^2). when you know that f(x)=1 , g(x)=2, f(x)prime=1/5, and g(x)prime=-5

Answer 1

\[h(x)=\sqrt{[f(x)]^2+[g(x)]^2}\]
\[h'(x)=\frac{1}{2}(2f(x) f'(x)+2g(x)g'(x))^\frac{-1}{2}\]

Answer 2

just plug in

Answer 3

and i'm sure those aren't the values for all x

Answer 4

this latex is not working for me :(

Answer 5

ya we were given a table of f and g values and their derivatives

Answer 6

i love those problems. use the formula, plug in the numbers

Answer 7

so i keep getting ((1/2)(Fx^2+gx^2)^(-1/2))*(2fx+gx)*(2fxprime +2gxprime) and idk waht im doing wrong

Answer 8

its the chain rule right?

Answer 9

when i put it in i get a nonreal answer and it will not take that

Answer 10

\[(f^2)'=2f^{2-1}f'=2ff'\]

Answer 11

so im typing the answer in as 1/(2(sqrt((2*1*(1/5)+(2*2*-5)))

Answer 12

\[(f^2+g^2)'=2ff'+2g g'\]

Answer 13

\[[(f^2+g^2)^\frac{1}{2}]'=\frac{1}{2}[(f^2+g^2)^{\frac{1}{2}-1}](2ff'+2g g')\]

Answer 14

\[=\frac{2ff'+2g g'}{2\sqrt{f^2+g^2}}=\frac{ff'+g g'}{\sqrt{f^2+g^2}}\]

Answer 15

f=1,g=2,f'=1/5, g'=-5
\[\frac{(1)(\frac{1}{5})+(2)(-5)}{\sqrt{(1)^2+(2)^2}}\]

Answer 16

\[=\frac{\frac{1}{5}-10}{\sqrt{1+4}}\]

Answer 17

\[=\frac{\frac{1-50}{5}}{\sqrt{5}}\]

Answer 18

good

Answer 19

haha ok that worked ty

Answer 20

=\[\frac{\frac{-49}{5}}{\sqrt{5}}\]
you got it?

Answer 21

but i dont really know why there is the part on the top and bottom

Answer 22

ohhhh i got it lol

Answer 23

what do you mean?

Answer 24

chain rule right?

Answer 25

yep

Answer 26

ty lol

Answer 27

we used a bunch of chain rule

Answer 28

ya i can see lol

Answer 29

good! :)

Answer 30

good rule that one

Answer 31

not so easy to prove though right?

Answer 32

what nilankshi?

Answer 33

bad copy and paste

Answer 34

therer is some prob with this page

Answer 35

oh is that what that is?

Answer 36

maybe mathml run amok

Answer 37

i can many symbol there

Answer 38

not again

Answer 39

lol

Answer 40

like this what is this

Answer 41

where are you trying to copy and paste from?

Answer 42

down