Consider x^3y=y^19x

Question

Use implicit differentiation to find dy/dx

Find the tangent equation at (1,1)

Answer 1

x³y = y¹⁹x

3x²y + x³(dy/dx) = 19y¹⁸(dy/dx)x + y¹⁹

x³(dy/dx) - 19xy¹⁸(dy/dx) = y¹⁹ - 3x²y

(dy/dx) [ x³ - 19xy¹⁸] = y¹⁹ - 3x²y

dy/dx = (y¹⁹ - 3x²y) / (x³ - 19xy¹⁸)