Question

Find dy/dx given
13√x + 8√y = 3.

Differentiate both sides of the equation with respect to x, and then solve for dy/dx. Do not substitute for y after solving for dy/dx.

dy/dx=_______

Super confused:( thank you!!

Answer 1

you're doing an implicit differentiation?

Answer 2

Soooo what are you stuck on? :U
The y term giving you trouble?

Answer 3

@celestialdictator i believe so... not sure the exact term

and @zepdrix i'm just not too sure where to start... am i setting it equal to zero?

Answer 4

write your radicals as exponents

Answer 5

well the derivative of a constant is always zero

Answer 6

so that right hand side is zero right away

Answer 7

ohh okay so would it be x^(1/13) and y^(1/8) ?

Answer 8

\[13x^{\frac{ 1 }{ 2 }}+8y^{\frac{ 1 }{ 2 }}=0\]

Answer 9

use the power rule to differentiate the left hand side
but when you differentiate the y, you have to write an extra y

Answer 10

ohh okay so from here, i rearrange it to look like this?

\[\frac{ 13 }{ 2\sqrt{x} } + \frac{ 8 }{ 2\sqrt{y} } \frac{ dy }{ dx } = 0\]

Answer 11

did i do that correctly?

Answer 12

oo good job! :)

Answer 13

yeah

Answer 14

then now, ask your self what is it that you wanted solved?

Answer 15

hehe thanks :)

so umm from here, would i isolate the dy/dx ?

Answer 16

yes

Answer 17

it's better to keep the radicals as exponents until the very end

Answer 18

okay, so would it look like this? \[\frac{ dy }{ dx }= - \frac{ 13\times2\sqrt{y} }{ 8\times2\sqrt{x} }\] :/

Answer 19

Looks good!!
Simplifyyyy \c:/

Answer 20

do i get \[-\frac{ 13\sqrt{y} }{ 8\sqrt{x} }\] ?

Answer 21

you tell us :P

Answer 22

haha umm i got that because the two 2's cancel out? would that be the final answer though? :/

Answer 23

Yah looks fine. You can combine the roots if you want,\[\Large\bf\sf -\frac{13}{8}\sqrt{\frac{y}{x}}\]Looks a little nicer.

Answer 24

looks a lot neater hehehe

Answer 25

ahh okay awesome!!! thank you both!!! :)

Answer 26

you didn't have to simplify, because it does not add or give any further information. it just makes equation look neater

Answer 27

when I become a professor, I wouldn't even ask my students to simplify. Just give me the correct answer and I would be satisfied

Answer 28

good job iheart and it's good that you're on calculus1 now

Answer 29

ohh okay cool :)

and yes!! i can assure you that the students will appreciate that!! :P

thank you :)