Question

Question 6: Find dy/dx : x³+ x²y + xy² + y³ = 81

Class 12 - Math - Continuity and Differentiability

Answer 1

Refer to the attachment

Answer 2

★ PARTIAL DIFFERENTIATION ★

Given composite function :

x^3 + x²y + xy² + y^3 = 81

Now differentiation of x with respect to y and secondary , differentiation of y with respect to x

dy/dx =( δx/δy) / ( δy/ δx )

δx/δy = 3x² + 2xy + y² = 0

δy/ δx = 0 + x² + 2xy + 3y² = 0

DIVISION will result the final output in partial differentiation

3x² + 2xy + y² / x² + 2xy + 3y²

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