Suppose f(t) and g(t) are single variable differentiable functions.Find ∂z∂x and ∂z∂y for each of the following binary functions. (a) z=f(x)g(y) (b) z=g(xy)

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Step 1: To deterine Given: Suppose f(t) and g(t) ate single variable differentiable functions. (a) z=f(x)g(y) (b) z=g(xy)     To deterine:  ∂z∂x&amp;amp; ∂z∂y Calculation: Since, f(x)g(y) Differentiating with respect to x, we get, ∂z∂x=∂∂x(f(x)g(y)) ∂z∂x=g(y)ddx(f(x))+f(x)ddx(g(y)) ∂z∂x=g(y)f‘(x)+f(x).0 ∂z∂x=g(y)f‘(x) Now differentiating with respect to y ∂z∂y=∂∂y(f(x)g(y)) ∂z∂y=g(y)∂∂y(f(x))+f(x)∂∂y(g(y)) ∂z∂y=g(y).0+f(x)g‘(y) ∂z∂y=f(x)g‘(y) Calculation: Since, z=g(xy) Differentiating with respect to x, we get, z=g(xy) Using chain rule, we have, ∂z∂x=∂∂x(g(xy)),∂∂x(xy) ∂z∂x=g‘(xy).y Now differentiating with respect to y ∂z∂y=∂∂y(g(xy)) Using chain rule, we have, ∂z∂x=∂∂y(g(xy)),∂∂y(xy) ∂z∂x=g‘(xy).x

Suppose f(t) and g(t) are single variable differentiable functions.Find \frac{\partial

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