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Chapter 2: Q. 57 (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鈥� 58. Your answers may involve r, s, q, or their derivatives.
$\frac{d}{d r} r s^{2}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given Information

We need to find $\frac{d}{dr} r s^{2} =$

Step 2. Finding Derivative

$\frac{d}{d r} r s^{2} = 1 s^{2} = s^{2}$

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Suppose f is a polynomial of degree n and let k be some integer with $0 鈮� k 鈮� n$ . Prove that if f(x) is of the form $f (x) = a_{n} x^{n} + a_{n - 1} x^{n - 1} + . . . . + a_{1} x + a_{0}$

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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鈥� 58. Your answers may involve r, s, q, or their derivatives.ddrrs2

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鈥� 58. Your answers may involve r, s, q, or their derivatives.
$\frac{d}{d r} r s^{2}$