Question

Could anyone help me with implicit differentiations?

Answer 1

Differentiate implicity to find dy/dx, then find the slope of the curve at the point.
y^2-x^3=1
(2,-3)

Answer 2

i'll give you an example

\[3x^2 + y^2 = 5 \rightarrow 6x + 2yy' = 0\]

Answer 3

@jim_thompson5910

Answer 4

differentiate both sides. remember when you differentiate y with respect to x, you must put dy/dx (or y', whichever convention you like)

in the above example

\[6x + 2yy' = 0 \rightarrow 2yy' = -6x \rightarrow y' = -\frac{ 3x }{ y }\]
and if we know a point, like (2, -3), we can determine the slope, y', by the above equation

Answer 5

treat y as an unknown function y(x). therefore, you must always apply chain rule.

for your example:

treat y^2 as (y(x))^2.

the derivative of that is 2y(x)*y'(x), which can be written more compactly as 2y*y'.

you will then want to put y' alone on one side. to find y' = implicit derivative

Answer 6

@Euler271 could you please help me? Assignment is due at 12 and I have no idea what I am doing

Answer 7

Like I will definitely have to learn this, but to learn this in 30 minutes and do the assignment is just too much:(

Answer 8

yes

\[y^2 - x^3 = 1\]
differntiate all with respect to x:\[2y*y' - 3x^2 = 0\]\[y' = \frac{ 3x^2 }{ 2y }\]

y' is the derivative function [the slope function]. plug in (x, y) = (2, -3)\[y' = \frac{ 3(2)^2 }{ 2(-3) } = -2\]

Answer 9

Okay and for this?
http://gyazo.com/3ff8663c8ec5e6d9050f88e30b79238b

Answer 10

2 is right lol

Answer 11

woohoo that was honestly a guess hahaha

Answer 12

And last one I think
http://gyazo.com/649bb6d25636232b40bc1a3ac3e5a253

Answer 13

C: 4.8

Answer 14

How so? I finished so i'd like to learn:)

Answer 15

we use the relationship of the length of the ladder and the wall (Pythagorean Theorem)

\[\frac{ d }{ dt }(L^2) = \frac{ d }{ dt }(x^2 + y^2)\]\[2L*L' = 2x*x' + 2y*y'\]L' = 0 beause the length of the ladder does not change
dx/dt = x' and dy/dt = y'

\[2(13)*0 = 2(5)dx/dt + 2(12)(-2)\]\[0 = 10dx/dt - 48\]\[\frac{ dx }{ dt } = 4.8\]

Answer 16

great. the drawing didn't work

Answer 17

Haha it's okay. Look at my newest question please, Hawk Crimson has been writing for like 10 minutes now.

Answer 18

the answer to that one is:\[\frac{ dy }{ dx } = y' = \frac{ 3x^2 +y^2 - 2xy - 1 }{ 1 - 2xy + x^2 + 3y^2 }\]

Answer 19

To this?:O
http://gyazo.com/d2824d641a3ef9e635f1e09fd2cc13ba

Answer 20

yes

Answer 21

But that's not an option :(

Answer 22

lol ill simplify it i guess

Answer 23

if its due live pick C

Answer 24

if you have time. give me a sec

Answer 25

actually B

Answer 26

I don't haha, times up! I got an 80 since I got that wrong, but whatever. Learning this kind of stuff within an hour is difficult >_< but B was wrong.

Answer 27

then c lol

Answer 28

not bad. do you have the answer?

Answer 29

Nope :(