Question

Find partial differential w/partial differential s and partial differential w/partial differential t using the appropriate Chain Rule. partial differential w/partial differential s = partial differential w/partial differential t= Evaluate each partial derivative when s = 2 and t = 3. partial differential w/partial differential s = partial differential w/partial differential t =?

Answer 1

To calculate the partial derivatives of w with respect to s and t, we need the specific function w(s,t) as well as the functions x(s,t) and y(s,t). Without this information, the exact values of the partial derivatives cannot be determined.

Step-by-step explanation:

To find the partial derivatives of the function w with respect to s and t, we would need the specific form of the function w(s,t). However, the question does not provide this information. Typically, the chain rule for partial differentiation states that if w is a function of x and y, where x and y are themselves functions of s and t, then:

• The partial derivative of w with respect to s is given by w_s = w_x × x_s + w_y × y_s.
• The partial derivative of w with respect to t is given by w_t = w_x × x_t + w_y × y_t.

To evaluate each partial derivative at s = 2 and t = 3, we would plug these values into the derived partial derivatives. Still, we would need the functional form of w and the respective derivatives of x and y with respect to s and t to proceed further.

Without this information, we cannot provide the exact values of partial differential w/partial differential s and partial differential w/partial differential t at the given points.