Answer
Verified
396.3k+ 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
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Using the following information to help you answer class 12 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE