Suppose that a function fxy where xxst and y yst you know th

Suppose that a function f(x,y), where x=x(s,t) and y =y(s,t), you know the following derivative values at a point (a,b):
(?f/?x)(a,b)= 1
(?f/?y)(a,b)= 2
(?x/?t)(a,b)= 3
(?y/?t)(a,b)= -1

find (?f/?t)(a,b)

Solution

f/t = (f/x)*(x/t) + (f/y)*(y/t) = (1*3) + (2*(-1)) = 3-2 = 1

Suppose that a function f(x,y), where x=x(s,t) and y =y(s,t), you know the following derivative values at a point (a,b): (?f/?x)(a,b)= 1 (?f/?y)(a,b)= 2 (?x/?t)

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