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The derivative of sec2 x with respect to tan2 x is

  1. 1
  2. 2
  3. 2 sec x tan x
  4. 2 sec2 x tan x

Answer (Detailed Solution Below)

Option 1 : 1
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Detailed Solution

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Concept:

Steps for derivatives of functions expressed in the parametric form:

  1. First of all, we write the given functions u and v in terms of the parameter x.
  2. Using differentiation find out du/dx and dv/dx.
  3. Then by using the formula used for solving functions in parametric form i.e.
  4.  Lastly substituting the values of du/dx and dv/dx and simplify to obtain the result.

Calculation:

Let u = sec2 x and v = tan2 x

Differentiating with respect to x, we get

 

Now,

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