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Chapter 2: Q 32. (page 222)

Find the derivatives of the functions: $f (x) = 11 + e^{π} - \ln 2$

Short Answer

Expert verified

The required answer is $0$ .

Step by step solution

Step 1. Given information.

The given function is: $f (x) = 11 + e^{π} - \ln 2$

Step 2. Find the derivative of the given function.

$f (x) = 11 + e^{π} - \ln 2 f' (x) = \frac{d}{d x} (11 + e^{π} - \ln 2)$

Since the derivatives of the constant term is role="math" localid="1648978915096" $0$ , so in the given question the terms are all constant term so the derivatives is $0$ .

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Most popular questions from this chapter

For each function $f (x)$ and interval localid="1648297458718" $[a, b]$ in Exercises localid="1648297462718" $81 - 86$ , use the Intermediate Value Theorem to argue that the function must have at least one real root on localid="1648297466951" $[a, b]$ . Then apply Newton’s method to approximate that root.

localid="1648297471865" $f (x) = x^{3} - 3 x + 1, [a, b] = [1, 2]$

In the text we noted that if $f (u (v (x)))$ was a composition of three functions, then its derivative is $\frac{d f}{d x} = \frac{d f}{d u} \times \frac{d u}{d v} \times \frac{d v}{d x}$ . Write this rule in “prime” notation.

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

$f (x) = \frac{x^{2} - \sqrt[3]{x} + 5 x^{9}}{\sqrt{x^{- 1}}}$

Use (a) the $h \to 0$ definition of the derivative and then

(b) the $z \to c$ definition of the derivative to find $f' (c)$ for each function f and value $x = c$ in Exercises 23–38.

24. $f (x) = x^{3}, x = 1$

Use the definition of the derivative to prove the following special case of the product rule

$\frac{d}{d x} (x^{2} f (x)) = 2 x f (x) + x^{2} f' (x)$

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Find the derivatives of the functions:f(x)=11+eπ-ln2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the derivative of the given function.

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Find the derivatives of the functions: $f (x) = 11 + e^{π} - \ln 2$