Question

y³+3y²-8y-3x³=-6 using the formula differentiation...​

Answer 1

Explanation:

★ 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