Chapter 2: Q. 67 (page 234)

Find the function from the given derivative
$f^{'} (x) = \frac{2}{\sqrt{1 - 4 x^{2}}}$

Short Answer

Expert verified

The function from given derivative is

$f (x) = \sin^{- 1} (2 x)$

Step by step solution

Step 1.Given information

We have been given derivative function

$f^{'} (x) = \frac{2}{\sqrt{1 - 4 x^{2}}}$

Step 2.Finding the function via approximation

One can suspect $\tan^{- 1} x$ from the given denominator

\begin{aligned} f (x) = \sin^{- 1} (2 x) \\ f (x) = \sin^{- 1} (2 x) \\ f^{'} (x) = \frac{1}{\sqrt{1 - (2 x)^{2}}} \frac{d}{d x} (2 x) \\ = \frac{2}{\sqrt{1 - 4 x^{2}}} \end{aligned}

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Find the function from the given derivative
$f^{'} (x) = \frac{2}{\sqrt{1 - 4 x^{2}}}$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Finding the function via approximation

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Find the function from the given derivativef′(x)=21−4x2

Short Answer

Step by step solution

Step 1.Given information

Step 2.Finding the function via approximation

One App. One Place for Learning.

Most popular questions from this chapter

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Find the function from the given derivative
$f^{'} (x) = \frac{2}{\sqrt{1 - 4 x^{2}}}$