Important Questions

CBSE Guess > Papers > Important Questions > Class XII > 2007 > Maths > Maths By : Mr. Deepak Sharma

Differentiation

Formulae use in Differentiation




 is also referred as f’(x).

  • Methods of Differentiation
  • Chain Rule is based upon the fact that  

Now if y = f (u) where u = g(x)
then = f’ (u) x g’ (u). For example

  • Differentiation of one function with respect to (w.r.t.) another function

    For example to differentiate tanx w.r.t. log x now let us consider u = tanx and v = logx.
  • Differentiation of implict function
    Derivative of f(y) with respect to x = f’(y)
    Derivative of f(y) with respect to y = f’(y)
    Derivative of f(x) with respect to x = f’(x)
    Derivative of f(x) with respect to x = f’(x)
  • Differentiation of parametric form
  • Application of log in differentiation
    1. log is applied if more than two variable are in multiplication and/or division.
    2. log is applied if variable comes as power except ex and ax .

For example if (application 1)

Now for example (application 2)

 We can not take log directly as there is –ve sign between two variables therefore let
y = u – v now

  • Differentiation of Inverse trigonometric function
    For Derivative of inverse trigonometric function following formulae are uses
    Inverse Trigonometric formulae
    Inverse formulae

Some inverse conversions


Some Substitutions

Then apply sin2½ x = (1-cosx)/2 = 2sin2x = 1 - cos2x

Some Trigonometric changes