Transcription of MATH 171 - Derivative Worksheet Differentiate these for fun ...
1 MATH 171 - Derivative WorksheetDifferentiate these for fun, or practice, whichever you need. The given answers are not (x) = 4x5 (x) = (x) = (x4+ 3x) (x) = 3x2(x3+ 1) (x) = cos4x (x) =x1 + (x)=x2 (x) = (3x2)(x12) (x) = ln(xe7x) (x) =2x4+ 3x2 (x)= (x3)5 2 (x) = 2x 4 (x) =4(3x 1)2x2+ (x)= x2+ (x)=x 1 (lnx) (x)=6(3x2 ) (x)=(3x2 x) (x) =x(x2+ 3x) (x)= (xex) (x)=[arctan(2x)] (x)= (e2x+e) (x) = (x6+ 1)5(4x+7) (x)= (7x+ x2+ 3) (x)=1x+1x2x (x) =3 x2 1 (x)= 2x+57x (x) = (x) =ex(x2+ 3)(x3+ 4) (x)=5x2 7xx2+ (x) =[ln(5x2+ 9)] (x)= ln(5x2+ 9) (x)= cot(6x) (x) = sec2x t (x) = arcsin(2x) (x)= tan(cosx) (x) = [(x2 1 )5 x] (x)= secx sin(3x) (x) =(x 1)3x(x+3) (x)
2 = log5(3x2+ 4x)In problems 40 42, a differentiable function 3y= +y2+x3= + 1=3xIffandgare differentiable functions such thatf(2) = 3 ,f (2) = 1,f (3) = 7 ,g(2) = 5andg (2) = 2 , find the numbers indicated in problems 43 (g f) (2)44. (fg) (2)45.(fg) (2)46. (5f+ 3g) (2)47. (f f) (2)48.(ff+g) (2)Answers:Absolutely not simplified .. you should simplify (x) = 20x4 (x) =excosx+ (sinx) (x) = 1(x4+ 3x) 2(4x3+ 3) (x) = 3x2 7(x3+ 1)6(3x2) + (x3+ 1)7 (x) = 4(cosx)3( sinx) (x) =(1 +x2)(1) x(2x)(1 +x2) (x) = 1 +x 2(Simplifyffirst.) (x) = 3 52x32(Simplifyffirst.) (x) =1x+ 7 (Simplifyffirst.)
3 (x) = 4x+ 0 + 2x 3(Simplifyffirst.) (x) =x3 15(2 x) 45( 1) + (2 x)15(3x2) (x) = 2 + 2x (x) =(x2+ 7x)[4 2(3x 1)(3)] 4(3x 1)2(2x+ 7xln 7)(x2+ 7x) (x) =12(x2+ 8) 12(2x) (x) =(1 (lnx)2)12(1) x 12(1 (lnx)2) 12( 2(lnx) 1x)1 (lnx) (x) = 24(3x2 ) 5(6x) (x) =16[4(3x2 x)3(6x )] (x) =(x2+ 3x)5(1) x[5(x2+ 3x)4(2x+12(3x) 12 3)](x2+ 3x) (x) = (xex)( 1)[xex+ex] (x) = 10[arctan(2x)]9 11 + (2x)2 (x) =12(e2x+e) 12(e2x 2 + 0) (x) = (x6+ 1)5[3(4x+ 7)2(4)]+ (4x+ 7)3[5(x6+ 1)4(6x5)] (x) = 6(7x+ x2+ 3)5(7 +12(x2+ 3) 12 2x) (x) =(x 1)( x 2 2x 3) (x 1+x 2)(1)(x 1) (x) =23x 13+32x (x) =12(2x+ 57x 9) 12[(7x 9)(2)]
4 (2x+ 5)(7)(7x 9)2] (x) = (x) =[ex(x2+ 3)](3x2) + (x3+ 4)[ex(2x) + (x2+ 3)ex] (x) =(x2+ 2)(10x 7) (5x2 7x)(2x)(x2+ 2) (x) = 3[ln(5x2+ 9)]2 15x2+ 9(10x+ 0) (x) =1(5x2+ 9)3 [3(5x2+ 9)2(10x+ 0)] (x) = csc2(6x) (x) = sec2x(sec2x) + tanx[2 secx(secxtanx)] (x) =1 1 (2x)2 2xln (x) =(sec2(cosx))( sinx) (x) = 3[(x2 1)5 x]2(5(x2 1)4 2x 1) (x) = secx(cos(3x) 3)+ sin(3x)(secxtanx) (x) =x(x+ 3)4[3(x 1)2(1)] (x 1)3[x 4(x+ 3)3(1) + (x+ 3)4(1)]x2(x+ 3) (x) =1(3x2+ 4x) ln 5 (6x+ 4) 3x2 yx+ (y2+ 1)2(y2+ 1)(cosy) 2ysiny43. 344. 1145. 12546. 147. 748. 14 Power. Product, and Quotient Rules Worksheet Find the Derivative of each function.
5 1. 2() 35 2fxxx= + 2. 43()452 3gxxxx= + + 3. 322() 27fxxxx=+ 4. 545() 87gxxxx= + 5. 2718()9xxfxx+ =+ 6. 2524()8xxfxx = 7. 33274()2xxxfxx + = 8. 273258()3xxxhxx+ = 9. 3( )2sec( )sxxx = 10. 4() 3xfxxe= 11. 3()7xfxxe= 12. 2() 5 cos()fxxx= 13. () 2xhxex= 14. 43 2() 452xfxxxxe= + 15. 2tan( )()21xfxx=+ 16. sin( )()5xxgxe=+ 17. 232()3xxfxx +=+ 18. 2()2xxefxxe= 19. 422cot( )()3xxhxx= 20. csc( )()4xxfxxe= AP Calculus AB Name _____ Chain Rule Worksheet Find the Derivative of each function.
6 1. 23( ) (25 )fxxx= 2. 3()52fxxx= 3. 3 sin(3)yx= 4. 22 cos(2)yx= + 5. 22( ) sin (3 )gxx= 6. 32( ) sec (5)hxx= 7. 32 5() 3xfxxe = 8. 223()5xxgxxe+= 9. 223 4 51yxxx= + 10. 332()353htttt= 11. 332141yxx= + 12. 343()2 53gttt =+ 13. ( ) sin(cos( ))gmm= 14. ( )cos(tan )fxx= 15. 324( )2 (1)hxxx=+ 16. 223( )1 (1)hmmm=++ 17. 2322()2tftt+= 18. 3438()8tftt+= 19. 74 5( )(25) (38)hxxx=+ 20. 23( )(32)(41)gnxx= + 21. 23( )csc ( )ftt= 22. 42( )cot (2 )ftt= 23. 322()xxhxe = 24.
7 243()xxfxe = 25. 323()52xhxx=+ 26. 3242()5sfsss= 27. 3sin() 5xfx= 28. 4() 2xefx=
