Question 6: Find dy/dx : x³+ x²y + xy² + y³ = 81
Class 12 - Math - Continuity and Differentiability
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★ 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
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
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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