Q 62. Find the derivative of given fun... [FREE SOLUTION]

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Chapter 2: Q 62. (page 234)

Find the derivative of given function
$f (x) = \cosh^{鈭� 1} 鈦� (\cosh^{鈭� 1} 鈦� x)$

Short Answer

Expert verified

The answer of this question is $= \frac{1}{(\sqrt{x^{2} 鈭� 1}) \sqrt{{(\cosh^{鈭� 1} 鈦� x)}^{2} 鈭� 1}}$

Step by step solution

Step 1.Given information

We have been given

f (x) = \cosh^{鈭� 1} 鈦� (\cosh^{鈭� 1} 鈦� x)

Step 2.Derivative of given function

Derivative of product function

(f g)^{鈥�} (x) = f^{鈥�} (x) g (x) + f (x) g^{鈥�} (x)

Derivative of quotient function

${(\frac{f}{g})}^{鈥�} (x) = \frac{f^{鈥�} (x) g (x) 鈭� f (x) g^{鈥�} (x)}{(g (x))^{2}}$

Chain rule of derivation

$(f 鈭� u)^{鈥�} (x) = f^{鈥�} (u (x)) u^{鈥�} (x)$

Solving we get

$\begin{aligned} \frac{d}{d x} (\sinh 鈦� x) = \cosh 鈦� x \\ \frac{d}{d x} (\cosh 鈦� x) = \sinh 鈦� x \\ \frac{d}{d x} (\tanh 鈦� x) = {sech}^{2} 鈦� x \\ \frac{d}{d x} (\sinh^{鈭� 1} 鈦� x) = \frac{1}{\sqrt{x^{2} + 1}} \\ \frac{d}{d x} (\cosh^{鈭� 1} 鈦� x) = \frac{1}{\sqrt{x^{2} 鈭� 1}} \\ \frac{d}{d x} (\tanh^{鈭� 1} 鈦� x) = \frac{1}{1 鈭� x^{2}} \end{aligned}$

Step 3. Using chain rule

$\begin{aligned} \frac{d}{d x} \cosh^{鈭� 1} 鈦� (\cosh^{鈭� 1} 鈦� x) = \frac{1}{\sqrt{{(\cosh^{鈭� 1} 鈦� x)}^{2} 鈭� 1}} (\frac{d}{d x} \cosh^{鈭� 1} 鈦� x) [Using chain rule] \\ = \frac{1}{\sqrt{{(\cosh^{鈭� 1} 鈦� x)}^{2} 鈭� 1} (\frac{1}{\sqrt{x^{2} 鈭� 1}})} \\ = \frac{1}{(\sqrt{x^{2} 鈭� 1}) \sqrt{{(\cosh^{鈭� 1} 鈦� x)}^{2} 鈭� 1}} \\ = \frac{1}{(\sqrt{x^{2} 鈭� 1}) \sqrt{{(\cosh^{鈭� 1} 鈦� x)}^{2} 鈭� 1}} \end{aligned}$

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91影视

Find the derivative of given function
$f (x) = \cosh^{鈭� 1} 鈦� (\cosh^{鈭� 1} 鈦� x)$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Derivative of given function

Step 3. Using chain rule

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91影视

Find the derivative of given functionf(x)=cosh鈭�1鈦�cosh鈭�1鈦�x

Short Answer

Step by step solution

Step 1.Given information

Step 2.Derivative of given function

Step 3. Using chain rule

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Calculus

Decision Maths

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the derivative of given function
$f (x) = \cosh^{鈭� 1} 鈦� (\cosh^{鈭� 1} 鈦� x)$