Question

How would I use implicit differentiation to derive y^4-2y=4x^3+x?

Answer 1

use chain rule :

\(\large (y^4)' = 4y^{4-1} y' = 4y^3 y'\)

Answer 2

for your given equation,
differentiate both sides with respect to x

Answer 3

\[\large y^4-2y=4x^3+x\]

differentiate both sides with respect to x :

\[\large 4y^3y'-2y'=4(3x^2)+1\]

Answer 4

isolate \(\large y'\) and you're done !

Answer 5

thank you so much!