Question

Use implicit differentiation to differentiate y=x^(8/37), by writing it as y^37=x^8.
Express your answer only in terms of x.

Answer 1

37y^36 y' = 8x^7
y' = 8/37 x^7/y^36

Now, since y^37 = x^8,
y^36 = (x^8)^(36/37)

y' = 8/37 x^7 x^(-288/37)
= 8/37 x^(-29/37)

Doing it explicitly, using the power rule,

y = 8/37 x^(8/37 - 1) = 8/37 x^(-29/37)

Kind of a dumb problem to use to illustrate implicit differentiation.