DHS Y4 Math 2 Supplementary Worksheet_Differentiation Techniques

Differentiation 2023_KhooGH_ Adapted from DHS materials 1 Year 4 Mathematics 2 Differentiation Supplementary Worksheet Name : ____________________________ ( ) Class : 4___ Date : _________ Chain Rule, Product Rule and Quotient Rule 1 Find d d y x for each of the following functions. (a) 1+= xy (b) 52 += xy (c) 1 1 2 + = x y (d) 3 23 −= xy (e) ( )( ) 2π 443y x x= − + (f) ( ) 221 xxy += (g) ( ) 7 12 −= xxy (h) 21 xxy += (i) 2 23 − += x xy (j) x xy 21 2 − −= (k) 1 21 xy x −= − (l) 2 21 1 xy x −= + Derivatives of Trigonometric Functions, Exponential Functions and Logarithmic Functions 2 Differentiate each of the following respect to x. (a) xxy 2tan2= (b) ( ) xxy 2sin2 5 −= (c) 13e xyx −= (d) ( ) 2e sin cosxy x x −=− (e) 2e 31 x y x= − (f) 2 2 cos e x xy= (g) 5ln 2 += xy (h)       − = 12 1ln 3x y (i) ( ) xxy 3ln1 23−=

Differentiation 2023_KhooGH_ Adapted from DHS materials 2 Miscellaneous Questions 3 Find the derivatives of the following (a) 32− = xy (b) 3 7xy = (c) 5 2 1 x y = (d) x xy 1+= (e) 232π πyx x=+ (f) x xy 28−= (g) 2 45 x xy −= (h) x xy 3 2150 2−= (i) x xy 32 2 −= (j) x xy 28−= (k) xxy −= 52 4 Differentiate the following with respect to x (a) x x 2 5− (b) 52 )132( +− xx (c) 2 2 3( 5 )xx− (d) 3 35 1 x− (e) xx 41)32( 2 −+ (f) x x 21 2 − − (g) )43cos(2 1 −x (h) xx 3tan2 (i) )3 π2(cos3 32 +xx (j) xx 2tane3 (k) 33ee e xx x− + (l) x x 2 )1(ln 3− , 01 x

Differentiation 2023_KhooGH_ Adapted from DHS materials 3 Answers 1(a) 1 21 x+ (b) 2 5 x x + (c) ( ) 32 1 x x − + (d) ( ) 23 1 32x− (e) ( )( )π 4 4 3 3 xx+− (f) 425 6 1xx++ (g) ( ) ( ) 6 2 1 16 1xx−− (h) 2 2 21 1 x x + + (i) ( ) 2 8 2x − − (j) ( ) 1 1 2 1 2 x xx +− −− (k) ( )2 1 2 1 xy xx = −− (l) ( ) ( ) 2 22 21 1 xx x +− + 2(a) 222 tan 2 2 sec 2x x x x + (b) ( ) ( ) 4 2 5sin 2 4cos 2 2 cos 2x x x x x− − + − (c) ( ) 13e 1x x− − (d) ( ) 2e 3cos sinx xx− − (e) ( ) ( ) 2 2 e 6 5 31 x x x − − (f) 2 2 sin 2 2cos e x xx+− (g) 2 5 x x + (h) 2 3 3 12 x x− (i) ( ) 3 32 11 6 ln 3 xx x x x  −− − + 3 (a) 53 2 3x − (b) 437 3 x (c) 75 2 5x − (d) 1 2 x xx − (e) ( ) 3 2 2π 16x x − (f) 2 8 x− (g) 3 85 x x − (h) 2 2 150 2 3 x x −− (i) 2 2 23x x + (j) 2 8 x− (k) ( )54 25 xx x − − 4 (a) 24 10 x − (b) )34()132(5 42 −+− xxx (c) 22 2(5 2 ) 3( 5 ) x xx − − (d) 43 )35( 1 x− (e) x xx 41 )110)(32(2 − ++− (f) 3)21( 1 x x − +− (g) )43(cos2 )43sin(3 2 − − x x (h) )3sec33(tan2 2 xxx+ (i)     +−++ )3 π2sin(3)3 π2cos()3 π2(cos6 2 xxxxx (j) )2sec22tan3(e 23 xxx + (k) )1(2 12 − + xx x (l) 43 2 34e (1 )(e ) e xxx x+−