Use implicit differentiation to find dy/dx:

Question

lnxy -y^3 = 10?

Answer 1

The equation is ln(xy) - y³ = 10.

Differentiate with respect to x.

(d/dx) [ln(xy) - y³] = (d/dx)(10)

(1/xy)[xy' + y] - 3y²y' = 0

(xy')/(xy) + y/(xy) - 3y²y' = 0

y'/y + 1/x - 3y²y' = 0

y'(1/y - 3y²) + 1/x = 0

y'(1/y - 3y²) = - 1/x

y' = - 1/x(1/y - 3y²)

y' = - y/(x - 3xy³)