Find $$f'\left( x \right)$$.$$f\left( x \right)=\sec x-\sqrt{2}\tan x$$

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Vedantu Content Team · Accepted Answer

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.

Find \[f'\left( x \right)\].
\[f\left( x \right)=\sec x-\sqrt{2}\tan x\]

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Find \[f'\left( x \right)\].\[f\left( x \right)=\sec x-\sqrt{2}\tan x\]

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