**Using the Chain Rule to Find Derivatives****Objective:**To use the chain rule to find the derivatives \(\frac{dz}{ds}\) and \(\frac{dz}{dt}\).**Given:**- You must demonstrate in your work that you are using the chain rule.- Equations: \[ z = x^2y + tx \] \[ x = s^2 + 3t \] \[ y = 25 - t \]**Instructions:**1. Identify the variables and their relationships: - \(z\) is a function of \(x\), \(y\), and \(t\). - \(x\) is a function of \(s\) and \(t\). - \(y\) is a function of \(t\).2. Apply the chain rule: - Differentiate \(z\) with respect to \(s\) and \(t\) by using the chain rule to incorporate the dependence of \(z\) on \(x\), \(y\), and directly on \(t\).3. For \(\frac{dz}{ds}\), consider how \(x\) and thus \(z\) changes with \(s\).4. For \(\frac{dz}{dt}\), account for the changes in \(x\), \(y\), and \(t\).**Note:**Organize your work clearly to demonstrate the use of the chain rule in obtaining derivatives.

Name: **Using the Chain Rule to Find Derivatives****Objective:**To use the
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: **Using the Chain Rule to Find Derivatives****Objective:**To use the chain rule to find the derivatives \(\frac{dz}{ds}\) and \(\frac{dz}{dt}\).**Given:**- You must demonstrate in your work that you are using the chain rule.- Equations: \[ z = x^2