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CBSE Guess > Papers > Important Questions > Class XII > 2007 > Maths > Maths By : Mr. Deepak Sharma
Differentiation
Formulae use in Differentiation
![](../../images/maths_08_clip_image002.gif)
![](../../images/maths_08_clip_image004.gif)
![](../../images/maths_08_clip_image006.gif)
is also referred as f’(x).
- Methods of Differentiation
- Chain Rule is based upon the fact that
![](../../images/maths_08_clip_image012.gif)
Now if y = f (u) where u = g(x) then = f’ (u) x g’ (u). For example
![](../../images/maths_08_clip_image015.gif)
- Differentiation of one function with respect to (w.r.t.) another function
![](../../images/maths_08_clip_image017.gif)
For example to differentiate tanx w.r.t. log x now let us consider u = tanx and v = logx.
![](../../images/maths_08_clip_image019.gif)
- Differentiation of implict function
Derivative of f(y) with respect to x = f’(y) ![](../../images/maths_08_clip_image008_0001.gif)
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) ![](../../images/maths_08_clip_image022.gif)
- Differentiation of parametric form
![](../../images/maths_08_clip_image024.gif)
- 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)
![](../../images/maths_08_clip_image026.gif)
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 ![](../../images/maths_08_clip_image030.gif)
![](../../images/maths_08_clip_image032.gif)
![](../../images/maths_08_clip_image034.gif)
- Differentiation of Inverse trigonometric function
For Derivative of inverse trigonometric function following formulae are uses Inverse Trigonometric formulae Inverse formulae
![](../../images/maths_08_clip_image036.gif)
Some inverse conversions
![](../../images/maths_08_clip_image038.gif)
Some Substitutions
![](../../images/maths_08_clip_image040.gif)
Then apply sin2½ x = (1-cosx)/2 = 2sin2x = 1 - cos2x
![](../../images/maths_08_clip_image042.gif)
Some Trigonometric changes
![](../../images/maths_08_clip_image044.gif)
![](../../images/maths_08_clip_image046.gif)
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