Question

Help is very appreciated!

Y is a differentiable function of x. Choose the alternative that is the derivative dy/dx.

x^3-y^3=1

x+cos(x+y)=0

3x^2-2xy+5y^2=1

I'm doing these for homework on my AP Calc preparation course and am really confused. The teacher kind of rushed over this and I don't really understand what they meant.

Thank You!

Answer 1

@ganeshie8 @myininaya @pooja195 @nincompoop @Preetha @phi

Answer 2

@Nnesha @mathstudent55 @e.mccormick @Loser66 @ash2326

Answer 3

Do you know partial derivative? implicit derivative?

Answer 4

sort of, we just started

Answer 5

the first one
x^3 +y^3 = 1
if we solve y w.r.t.x, it is hard to take derivative. Hence, we apply implicit one
derivative both sides
3x^2 + 3y^2y' =0
that gives us y'= -x^2/y
right?

Answer 6

that is it.

Answer 7

oh, cool

Answer 8

would it be positive?

Answer 9

oh wait, nvm

Answer 10

for the second one
x +cos (x+y) =0
same
1-sin(x+y) *(x+y)' =0
1+ sin(x+y)(1+y') =0
so, just solve for y'
that is it.
do the same with the rest/

Answer 11

oh, I mess up at the second line, it is 1- sin...

Answer 12

Oh, gotcha. Is it okay if you help me with another question?

If x=e^theta cos theta and y=e^theta sin theta, then, when theta=pi/2, dy/dx is...