Answer
424.2k+ views
Hint: To solve the above problem first we have to find the basic derivatives of \[\sec x\] and \[\tan x\]. After substituting the derivatives in the equation, rewrite the equation with the derivatives of the function. Solve the equation to find the final answer.
Complete step-by-step answer:
Applying derivative on both sides of the equation with respect to x we get,
\[f'\left( x \right)=\dfrac{d}{dx}\left( \sec x \right)-\dfrac{d}{dx}\left( \sqrt{2}\tan x \right)\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
We know the derivative of \[\sec x\] is \[\sec x\cdot \tan x\] and the derivative of \[\tan x\] is \[{{\sec }^{2}}x\].
On substituting the derivatives of \[\sec x\] and \[\tan x\] in the above equation we get,
\[f'\left( x \right)=\sec x\cdot \tan x-\sqrt{2}{{\sec }^{2}}x\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
Taking \[\sec x\] as common in the right hand side (RHS) we get,
\[f'\left( x \right)=\sec x\left( \tan x-\sqrt{2}\sec x \right)\]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)
Hence the value of \[f'\left( x \right)\] is \[\sec x\left( \tan x-\sqrt{2}\sec x \right)\].
Note: The possible error that you may encounter can be the wrong substitution values of the derivatives of \[\sec x\] and \[\tan x\]. Solving the equation should be done carefully. It is to note here that integers are exempted from the calculation of derivatives.
Complete step-by-step answer:
Applying derivative on both sides of the equation with respect to x we get,
\[f'\left( x \right)=\dfrac{d}{dx}\left( \sec x \right)-\dfrac{d}{dx}\left( \sqrt{2}\tan x \right)\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
We know the derivative of \[\sec x\] is \[\sec x\cdot \tan x\] and the derivative of \[\tan x\] is \[{{\sec }^{2}}x\].
On substituting the derivatives of \[\sec x\] and \[\tan x\] in the above equation we get,
\[f'\left( x \right)=\sec x\cdot \tan x-\sqrt{2}{{\sec }^{2}}x\] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)
Taking \[\sec x\] as common in the right hand side (RHS) we get,
\[f'\left( x \right)=\sec x\left( \tan x-\sqrt{2}\sec x \right)\]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)
Hence the value of \[f'\left( x \right)\] is \[\sec x\left( \tan x-\sqrt{2}\sec x \right)\].
Note: The possible error that you may encounter can be the wrong substitution values of the derivatives of \[\sec x\] and \[\tan x\]. Solving the equation should be done carefully. It is to note here that integers are exempted from the calculation of derivatives.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)