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Chapter 2: Q 33. (page 237)

Fill in the blank:
$\frac{d}{d x} (s e c^{- 1} x) = - - -$

Short Answer

Expert verified

$\frac{d}{d x} (s e c^{- 1} x) = \frac{1}{|x| \sqrt{x^{2} - 1}}$

Step by step solution

01

Given Information

The given expression is $\frac{d}{d x} (s e c^{- 1} x)$

02

Simplification

Differentiation of $s e c^{- 1} x$ is $\frac{1}{|x| \sqrt{x^{2} - 1}}$

$\Rightarrow \frac{d}{d x} (s e c^{- 1} x) = \frac{1}{|x| \sqrt{x^{2} - 1}}$

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Most popular questions from this chapter

State the chain rule for differentiating a composition $g (h (x))$ of two functions expressed

(a) in “prime” notation and

(b) in Leibniz notation.

Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

Use the $h \to 0$ definition of the derivative to prove the power rule holds for positive integers powers

For each function f and value $x = c$ in Exercises 35–44, use a sequence of approximations to estimate $f' (c)$ . Illustrate your work with an appropriate sequence of graphs of secant lines.

$f (x) = 4 - x^{2}, c = 1$

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The tangent line to $f (x) = x^{2}$ at $x = 0$

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