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CBSE Class 12-science Answered

Define quotient rule, product rule, and chain rule .
Asked by NAKSHATRA | 01 Dec, 2014, 09:24: AM
answered-by-expert Expert Answer
Q u o t i e n t space r u l e : L e t space f open parentheses x close parentheses space a n d space g open parentheses x close parentheses space b e space t w o space f u n c t i o n s. L e t space h open parentheses x close parentheses equals fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction G i v e n space y equals h open parentheses x close parentheses fraction numerator d y over denominator d x end fraction equals fraction numerator d h over denominator d x end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator d over denominator d x end fraction open square brackets fraction numerator f open parentheses x close parentheses over denominator g open parentheses x close parentheses end fraction close square brackets rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator g open parentheses x close parentheses cross times begin display style fraction numerator d f open parentheses x close parentheses over denominator d x end fraction end style minus f open parentheses x close parentheses cross times fraction numerator d g open parentheses x close parentheses over denominator d x end fraction over denominator g open parentheses x close parentheses squared end fraction P r o d u c t space r u l e : L e t space f open parentheses x close parentheses space a n d space g open parentheses x close parentheses space b e space t w o space f u n c t i o n s. L e t space h open parentheses x close parentheses equals f open parentheses x close parentheses cross times g open parentheses x close parentheses G i v e n space y equals h open parentheses x close parentheses fraction numerator d y over denominator d x end fraction equals fraction numerator d h over denominator d x end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator d over denominator d x end fraction open square brackets f open parentheses x close parentheses cross times g open parentheses x close parentheses close square brackets rightwards double arrow fraction numerator d y over denominator d x end fraction equals f open parentheses x close parentheses cross times fraction numerator d g open parentheses x close parentheses over denominator d x end fraction plus g open parentheses x close parentheses cross times fraction numerator d f open parentheses x close parentheses over denominator d x end fraction C h a i n space r u l e : L e t space f open parentheses x close parentheses space a n d space g open parentheses x close parentheses space b e space t w o space f u n c t i o n s. L e t space y open parentheses x close parentheses equals open parentheses f ring operator g close parentheses open parentheses x close parentheses rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator d over denominator d x end fraction open parentheses f ring operator g close parentheses open parentheses x close parentheses rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator d over denominator d x end fraction open parentheses f open parentheses g open parentheses x close parentheses close parentheses close parentheses rightwards double arrow fraction numerator d y over denominator d x end fraction equals f open parentheses g open parentheses x close parentheses close parentheses apostrophe rightwards double arrow fraction numerator d y over denominator d x end fraction equals f apostrophe open parentheses g open parentheses x close parentheses close parentheses cross times g apostrophe open parentheses x close parentheses
Answered by Vimala Ramamurthy | 02 Dec, 2014, 10:41: AM

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CBSE 12-science - Maths
Differetion of Sin x
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If x= 2t/1+t^2 ,y=1-t^2/1+t^2 then Dy/DX +x/y is (A) 1 (B) 2 (C) 0 (D)4t^2
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If x = (2cos thita  - cos 2 thita)   and y = (2sin thita – sin 2 thita) find d2y/dx2 at thita = pie/2 Explain in great detail
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