Chain Rule with Inverse Trig - Kuta Software

[Pages:2]Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Inverse Trigonometric Functions

Date________________ Period____

Differentiate each function with respect to x.

1) y = cos-1 -5x3

2) y = sin-1 -2x2

3) y = tan-1 2x4

4) y = csc-1 4x2

5) y = (sin-1 ) 5x2 3

6) y = sin-1 (3x5 + 1)3

7) y = (cos-1 ) 4x2 2

8) y = cos-1 (-2x3 - 3)3

?9 L2d0J1s2x hKLuAtaaf qSHoIf3t2wKaBr4eH nLZLzCs.N k qAilul5 NroiYghhZtDsN WrzezsRecr9vverdF.r C 2MEatdseN Ww4i2tuhc VIenIfeiBnMiVtaeU NCDaflcckujlPujsK.m

Worksheet by Kuta Software LLC

Kuta Software - Infinite Calculus

Name___________________________________

Differentiation - Inverse Trigonometric Functions

Date________________ Period____

Differentiate each function with respect to x.

1) y = cos-1 -5x3

2) y = sin-1 -2x2

dy = -

1

-15x2

dx

1 - (-5x3)2

15 x2 =

1 - 25x6

dy

1

=

-4x

dx 1 - (-2x2)2

4 x = -

1 - 4x4

3) y = tan-1 2x4

dy =

1

8x3

dx (2x4)2 + 1

8x3 = 4x8 + 1

4) y = csc-1 4x2

dy

1

= -

8x

dx

4x2 (4x2)2 - 1

2 = -

x 16x4 - 1

5) y = (sin-1 ) 5x2 3

dy = 3 (sin-1 ) 5x2 2

1

10x

dx

1 - (5x2)2

30x (sin-1 ) 5x2 2

= 1 - 25x4

6) y = sin-1 (3x5 + 1)3

dy =

1

3(3x5 + 1)2 15x4

dx 1 - ((3x5 + 1)3)2

45x4(3x5 + 1)2

=

1 - (3x5 + 1)6

7) y = (cos-1 ) 4x2 2

dy = 2cos-1 4x2 -

1

8x

dx

1 - (4x2)2

16xcos-1 4x2 = -

1 - 16x4

8) y = cos-1 (-2x3 - 3)3

dy = -

1

3(-2x3 - 3)2 -6x2

dx

1 - ((-2x3 - 3)3)2

18x2(-2x3 - 3)2

=

1 - (-2x3 - 3)6

Create your own worksheets like this one with Infinite Calculus. Free trial available at

?M 62C0h1o26 DKfuntHaZ gSMoWfStbwbaPrOeD FLmLgCT.g P EAmlXl8 3ruiCgxhqtNs1 4rue1sEe3rIv0eCdo.w Z fMGa2dBeR cwyi7tnhW iIOnkf3iKnwigt7eJ iCuaulNcvuHlWuRsU.B

Worksheet by Kuta Software LLC

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download