# assignment2 - ma2176 a2 1 Derivatives If y = x sin x prove...

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1 ma2176 a2 Derivatives 1. If sin yx x = , prove that ( ) 22 '' 2 ' 2 0 xy x y x y −+ + = . 2. If c bx ax u + + = 2 2 , prove that u c bx ax xu dx d + + = 3 2 ) ( 2 . 3. Differentiate the following functions with respect to x : (a) () 3000 2 12 5 xx +− , (b) ( ) ( ) 33 sin 2 5cos 1 + , (c) ( ) ln ln ln x . 4. Find the values of a and b (in terms of c ) such that ) ( ' c f exists, where + > = c x b ax c x |x| x f | | if | | if 1 ) ( . 5. A function y of x is defined by the equation sin( ) sin x ymy = . Express y explicitly in terms of x . Hence, or otherwise, show that 2 cos 2 1 cos 1 m x m x m dx dy + + + = . 6. Let cot 1 x yx =+ , find
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• Spring '08
• LUI
• Mathematical analysis, Logarithm, Graph of a function, Parametric equation, following functions, Vector-valued function

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