Question

Use implicit differentiation

Answer 1

\[x^2+y=x^3+y^3\]

Answer 2

\[2x+y'=3x^2+3y^2y'\] then algebra to solve for
\[y'\]

Answer 3

ok im not sure why y goes to y prime rather than dy/dx this confuses me why does it sometimes go to dy/dx and others it goes to y^1

Answer 4

they are synonyms
\[x^2+f(x)=x^3+f^3(x)\]

Answer 5

y'=dy/dx

Answer 6

easier for me to write
\[y'\] than it is to write
\[\frac{dy}{dx}\]

Answer 7

both same

Answer 8

so there is literally no difference because my book uses both

Answer 9

no difference at all

Answer 10

haha ok, and when you divide yprime by yprime you get y prime?

Answer 11

like saying
\[f(x)=x^2,f'(x)=2x\] or
\[f(x)=x^2\]
\[\frac{dy}{dx}=2x

Answer 12

can use prime notation or leibniz notation they mean the same thing (mostly)

Answer 13

well ok now I've got it down to y^1=3x^2-2x+3y^2(y^1) do i just divide all by y prime?