Using chain rule of differentiation,
find
i) d/dx cos open parentheses y squared close parentheses
ii) d/dx cos squared open parentheses y close parentheses
    & sin open parentheses y squared close parentheses
iii) d/dx y to the power of x
stepwise

Asked by vicky Sekaran | 13th Apr, 2015, 08:13: PM

Expert Answer:

left parenthesis i right parenthesis fraction numerator d over denominator d x end fraction cos open parentheses y squared close parentheses equals negative sin open parentheses y squared close parentheses cross times 2 y cross times fraction numerator d y over denominator d x end fraction left parenthesis i i right parenthesis fraction numerator d over denominator d x end fraction cos squared open parentheses y close parentheses equals 2 cos y cross times open parentheses negative sin y close parentheses cross times fraction numerator d y over denominator d x end fraction fraction numerator d over denominator d x end fraction sin squared open parentheses y close parentheses equals 2 sin y cross times open parentheses cos y close parentheses cross times fraction numerator d y over denominator d x end fraction left parenthesis i i i right parenthesis C o n s i d e r space g open parentheses x close parentheses equals y to the power of x T a k i n g space log a r i t h m space o n space b o t h space t h e space s i d e s comma space w e space h a v e comma ln open parentheses g open parentheses x close parentheses close parentheses equals x cross times ln y D i f f e r e n t i a t i n g space t h e space a b o v e space e q u a t i o n space w i t h space r e s p e c t space t o space x comma space w e space h a v e comma fraction numerator d over denominator d x end fraction open parentheses g open parentheses x close parentheses close parentheses equals x cross times 1 over y cross times fraction numerator d y over denominator d x end fraction plus ln y cross times 1 T h u s comma fraction numerator d over denominator d x end fraction open parentheses y to the power of x close parentheses equals x over y cross times fraction numerator d y over denominator d x end fraction plus ln y

Answered by Vimala Ramamurthy | 15th Apr, 2015, 09:03: AM

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