Chapter 2: Q. 38 (page 233)

Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra
$f (x) = 3 {(\sin^{- 1} x)}^{2}$

Short Answer

Expert verified

The derivative of the function is $\frac{6 \sin^{- 1} x}{\sqrt{1 - x^{2}}} .$

Step by step solution

Step 1. Given Information.

The given function is $f (x) = 3 {(\sin^{- 1} x)}^{2}$ .

Step 2. Preliminary Algebra.

We know,

$(f g)^{'} (x) = f^{'} (x) g (x) + f (x) g^{'} (x) {(\frac{f}{g})}^{'} (x) = \frac{f^{'} (x) g (x) - f (x) g^{'} (x)}{(g (x))^{2}} (f \circ u)^{'} (x) = f^{'} (u (x)) u^{'} (x)$

Step 3. Derivative of the function.

The derivative of the function will be,

$f' (x) = \frac{d}{d x} 3 {(\sin^{- 1} x)}^{2} = 3 (2 \sin^{- 1} x \frac{d}{d x} (\sin^{- 1} x)) [Using chain rule] = 3 ((2 \sin^{- 1} x) \frac{1}{\sqrt{1 - x^{2}}}) = \frac{6 \sin^{- 1} x}{\sqrt{1 - x^{2}}}$

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Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra
$f (x) = 3 {(\sin^{- 1} x)}^{2}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Preliminary Algebra.

Step 3. Derivative of the function.

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Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebraf(x)=3sin-1x2

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Preliminary Algebra.

Step 3. Derivative of the function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Geometry

Statistics

Study anywhere. Anytime. Across all devices.

Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra
$f (x) = 3 {(\sin^{- 1} x)}^{2}$