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