Notes_Exercises_Set02

# Notes_Exercises_Set02 - 1 Derivative of a constant Rule D...

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Derivative of a constant Rule: 0 ] [ = c D x * 0 0 lim lim ] [ 0 0 = Δ = Δ - = Δ Δ x x c c c D x x x 2. Derivative of Basic Functions: 1 ] [ = x D x , x x D x 2 ] [ 2 = , x x D x 2 1 ] [ = , 2 1 ] 1 [ x x D x - = * 1 1 lim lim ) ( lim ] [ 0 0 0 = = Δ Δ = Δ - Δ + = Δ Δ Δ x x x x x x x x x x x D * 2 0 0 0 1 ) ( lim ) ( ) ( lim 1 1 lim ] 1 [ x x x x x x x x x x x x x x x x x x D x x x x - = Δ + Δ Δ - = Δ Δ + Δ + - = Δ - Δ + = Δ Δ Δ 3. Power Rule : 1 ] [ - = n n x nx x D , where n is a Real No. Ex: 2 3 3 ] [ x x D x = , 9 / 11 1 9 / 2 9 / 2 9 2 9 2 ] [ x x x D x - = - = - - - 1 2 5 2 5 5 2 ] [ - = x x D x 4. Derivative of exponential function: x x x e e D = ] [ , ) ln( ] [ a a a D x x x = (proofs will be supplied later) 5. Derivative of logarithmic function: x x D x 1 )] [ln( = , ) ln( 1 ] [log a x x D a x = (proofs will be supplied later) 6. Derivative of Trigonometric Functions: ) cos( )] [sin( x x D x = , ) ( sec )] [tan( 2 x x D x = ) tan( ) sec( )] [sec( x x x D x = ) sin( )] [cos( x x D x - = , ) ( csc )] [cot( 2 x x D x - = ) cot( ) csc( )] [csc( x x x D x - = (proofs will be supplied later) 7. Coefficient Rule: ' ] [ cf cf D x = ' )] ( ) ( [ lim )] ( ) ( [ lim ) ( ) ( lim ] [ 0 0 0 cf x x f x x f c

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Notes_Exercises_Set02 - 1 Derivative of a constant Rule D...

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