Question

x² + y² = (X+Y)^xy differentiate
​

Answer 1

apply log

log(x²+y²) = xylog(X+y)

differentiate on both sides

1/(x²+y²) d/dx (x²+y²) = ylog(X+y) + xy'log(X+y) + xy(1/X+y) (1+y')

1/(x²+y²) (2x)(2y)y' = ylog(X+y) + xy'log(X+y) + xy(1+y')/X+y

4xyy'/x²+y² = log(X+y) { y + xy'} + xy(1+y')/x+y