Show that the function f(x,y)=xy-7y2 is differentiable by finding values of 1 and 2 that satisfy the following definition.Definition: If z=f(x,y), then f is differentiable at (a,b) if z can be expressed in the formz=fx(a,b)xfy(a,b)yt1xt2y, where 1 and t20as(x,y)(0,0)To find an expression for z, we choose an arbitrary point (a,b), another point arbitrarily close to the first (ax,by), and compute the difference between their respective f-values.z=f(ax,by)-f(a,b)=(ax)(by)-7(by)2-(,)=abaybxxy-7b2-14by-7(y)2-ab()=()ybxxy-()yy, but fx(a,b)= and fy(a,b)=,so z=fx(a,b)xfy(a,b)yxy-7yy.000RelationsSetsVectorsTrigGreekHateLet t1=y and 2=-7y, therefore f is differentiable by the given definition.Need Help?