Find dy/dx for the following functions: (i) xy – tan(xy) (ii) x^2 – xy + y^2 = 1 (iii) x^3 + y^3 + 3axy = 1

Question

Find \(\frac{dy}{dx}\) for the following functions:

(i) xy – tan(xy)

(ii) x² – xy + y² = 1 

(iii) x³ + y³ + 3axy = 1

Answer 1

(i) Given xy = tan(xy) 

Differentiating both sides with respect to x, we get

(ii) x² – xy + y² = 7 

Differentiating both side with respect to x,

(iii) x³ + y³ + 3axy = 1 

Differentiating both sides with respect to x,