7. Suppose that f : R2 -+ R2 has continuous first-order partial derivatives in some ball Br(xo, Yo), r > o. Prove that if 6. j (xo, Yo) i= 0, then 8f11 (f( )) = 8h/8y(xo, Yo)

uJ;lX xo, Yo tA.. ..J(. jXo,Yo )'

8f11 (f( )) _ -8fr/8y(xo, yo)

J;l Xo, Yo - A ( )' uy t....J.j Xo, Yo and 8f;1 (f( )) = -8h/8x(xo,yo)

uJ;lX Xo, Yo tA.. ..J(. jXo,Yo )'

-8f;-1 (f( xo,Yo )) -_ 8fr/8x(xo, Yo)