Question

Suppose y =f(x(s,t),y(s,t)), and suppose that df/dt = 10, df/dx = 2, df/dy = 1, dx/ds = -3, dx/dt = 4 and dy/ds = 5 find the value of dy/dt.

Show work please.

Answer 1

To find dy/dt, we use the chain rule. The answer is 2, found by solving the equation 10 = (2)*(4) + (1)*(dy/dt).

Step-by-step explanation:

The student is asking about partial differentiation in a multivariable function: y = f(x(s,t), y(s,t)). Given partial derivatives of f with respect to t, x, and y, and given derivatives of x and y with respect to s, we need to find the derivatives of y with respect to t. By applying the chain rule:

1. df/dt = (df/dx)*(dx/dt) + (df/dy)*(dy/dt)
2. 10 = (2)*(4) + (1)*(dy/dt)
3. 10 = 8 + (dy/dt)
4. dy/dt = 10 - 8
5. dy/dt = 2

Hence, the value of dy/dt is 2.