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Differentiate the following function with respect to t. w= f(x,y) = x2−xy+y2, where x = g(t)=4t3 and y=h(t) = cost answer: solution: if w=f(x,y) , x=g(t) and y=h(t) then by chain rule in function of one variable then….. dw/dt= dw/dx . dx/dt + dw/dy. dy/dt Here we have w = x2 – xy + y2 , x= 4t3 ,y=cost dw/dx= d/dx ( x2 – xy + y2 ) dw/dx = 2x-y+ y2……………(i) dx/dt = d/dx (4t3) dx/dt =12t2…………….(ii) dw/dy = d/dx ( x2 – xy + y2 ) dw/dy = x2 – x + 2y………………..(iii) dy/dt = d/dx (cost) dy/dt = - sint…………………..(iv)
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