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Chapter 2: Q. 53 (page 210)

Suppose that r is an independent variable, s is a function of r, and q is a constant. Calculate the derivatives in Exercises 53– 58. Your answers may involve r, s, q, or their derivatives.
$\frac{d}{d r} s^{3}$

Short Answer

Expert verified

Thus, $\frac{d}{d r} s^{3} = 3 s^{2} \frac{d s}{d r}$

Step by step solution

Step 1. Given Information

We need to find $\frac{d}{d r} s^{3}$

Step 2. Finding Derivative

$\frac{d}{d r} s^{3} = 3 s^{2} \frac{d s}{d r}$

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Most popular questions from this chapter

A tomato plant given $x$ ounces of fertilizer will successfully bear $T (x)$ pounds of tomatoes in a growing season.

(a) In real-world terms, what does $T (5)$ represent and what are its units? What does $T' (5)$ represent and what are its units?

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Suppose that r is an independent variable, s is a function of r, and q is a constant. Calculate the derivatives in Exercises 53– 58. Your answers may involve r, s, q, or their derivatives.ddrs3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding Derivative

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Suppose that r is an independent variable, s is a function of r, and q is a constant. Calculate the derivatives in Exercises 53– 58. Your answers may involve r, s, q, or their derivatives.
$\frac{d}{d r} s^{3}$