BASIC DIFFERENTIATION

Assignment for basic differentiation Type I Problems based on fundamental results Q 1. Differentiate the Functions w.r.t x. 1. 11 4 sin 2 3 2 31 + - + x x x 2. x d cx bx ax + + + 2 3 3. 2 1     + x x 4. x x x x 3 cos 3 2 2 2 + + + 5. 2 3 ) 2 )( 1 ( x x x - + 6.     +     + x x x x 1 1 Q 2. Find of the following. ) 2 ( ) 2 )( 1 ( . 1 2 3 - - - + = x x x x y n n n n n a x a x a x a x a y + + + + + = - - - 1 2 2 1 1 0 ... .......... . 2 Where, s a i ' are real no.s and 0 ¹ n a . ) cos( . 3 a x y + = x a x y cos ) sin( . 4 + = aa cos cos 2 cos 2 cos . 5 -- = xx y x x y sincos 2 . 6 - = 11 cos 5 cot 3 . 7 - + = ecx x y x c x b x a y sin cos sin . 8 + - = x a y x log 2 3 . 9 + = ecx x e y x cos 2 sin . 10 + + = Type II Problems based on Product Rule Find of the following. x x y log . 1 2 = ecx x y cos . 2 3 = x y 2 sin . 3 = x x y 1 tan log . 4 - = x x y 1 cos sin . 5 - = x x y tan 2 cos . 6 = x x x x y cot log . 7 4 24 + = x x x y log sec . 8 1 4 - = x x x y tan sin . 9 2 = x x x y sec sin log . 10 = Type III Problems based on Quotient rule Find of the following xx y cos 1 cos 1 . 1 -+ = x x y sin 1 cos . 2 + = r qx px b ax y + ++ = 2 . 3 x x x x y cos sin cos sin . 4 -+ = Assignment for basic differentiation x x x y sincos . 5 5 - = a x a x y n n -- = . 6 x x x x y sin 1 sec . 7 2 1 2 + + = - x x x x y cos 7 3 sin 5 4 . 8 ++ = x x x e y x tan cot tan . 9 - + = x a x x y x tan log . 10 = Type IV Problems based on Composite Functions or Chain rule Find of the following x y sin log . 1 = 2 cot log . 2 x y = x a e y = . 3 ) sin(log . 4 x y = x y sin sin . 5 = x x x e y x sincos . 6 2 × = - ) tan log(sec . 7 x x y + = ) 2 cos 2 log(sin . 8 x x y + = ax a x a x y 1 2 2 2 sin 2 . 9 - + - = ) sin( 24 . 10 2 sin x x x a y + = x x e y sin . 11 = x y 3 sin . 12 = 3 2 sin . 13 x y = 2 ) sin (log . 14 x y = ) log(log . 15 log x e y x + = Type V Problems based on Implicit Functions Find of the following (1) y = mx + c (2) 4(3) 2220 (4) x√= √(5) x cos + y cos = tan) (6)log (7) !log + sin "