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The problem in the image asks for the value of \(\frac{dp}{ds}\) given the values \(\frac{dp}{dt} = 3\) and \(\frac{dt}{ds} = 0.6\).

To find \(\frac{dp}{ds}\), we can use the chain rule of differentiation:

\[
\frac{dp}{ds} = \frac{dp}{dt} \times \frac{dt}{ds}
\]

Substituting the given values:

\[
\frac{dp}{ds} = 3 \times 0.6 = 1.8
\]

Thus, \(\frac{dp}{ds} = 1.8\).

Would you like any further details or have any questions about this solution?

Here are five related questions you might find useful:
1. What is the chain rule in calculus, and how is it generally applied?
2. How does the chain rule extend to functions of multiple variables?
3. Can you explain the concept of implicit differentiation and how it relates to the chain rule?
4. How do we interpret the result of \(\frac{dp}{ds} = 1.8\) in practical terms?
5. What are some common mistakes to avoid when using the chain rule?

**Tip:** When applying the chain rule, ensure that the intermediate derivatives (like \(\frac{dp}{dt}\) and \(\frac{dt}{ds}\)) are correctly oriented to match the variables in the final derivative you seek.

If \(\frac{dp}{dt} = 3\) and \(\frac{dt}{ds} = 0.6\), what is \(\frac{dp}{ds}\)?

Learn how to find the derivative \(\frac{dp}{ds}\) given \(\frac{dp}{dt} = 3\) and \(\frac{dt}{ds} = 0.6\) using the chain rule of differentiation. This problem is suitable for college-level calculus students.

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