1. let f(x, y) be a differentiable function in the variables x and y. let r and θ the polar coordinates, and set g(r, θ) = f(r cos θ, r sin θ) in other words g is f in terms of polar coordinates. suppose that it is known that fx(1, 1) = −2 and fy(1, 1) = 3 use the chain rule in order to compute the partial derivative gr( √ 2, π/4).

Step-by-step explanation:

First, notice that:

We proceed to use the chain rule to find using the fact that to find their derivatives:

Because we know then:

We substitute in what we had:

Now we put in the values in the formula:

Because of what we supposed:

And we operate to discover that:

and this will be our answer

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step-by-step explanation: