Derivatives of Inverse Functions PDF

Kuta Software - Infinite Calculus Name___________________________________ Derivatives of Inverse Functions...

Kuta Software - Infinite Calculus Name___________________________________ Derivatives of Inverse Functions Date________________ Period____ For each problem, find ( f )' ( x) by direct computation. −1 1) f ( x) = −3 x + 3 2) f ( x) = −2 x + 3 1 For each problem, find ( f )' ( x) by using the theorem ( f −1)' ( x) = −1 f '( f ( x) ) −1 3) f ( x) = −5 x + 1 4) f ( x) = −2 x + 2 5) f ( x) = −2 x − 3 6) f ( x) = −4 x 3 − 4 For each problem, find ( f −1 )' ( x) by using the formula dy = 1 −1 , where y = f ( x) dx dx dy 7) f ( x) = x 7 + x − 3 8) f ( x) = 3 x 5 + 2 x + 5 ©U P24021V3P nKYuGtwam kSBocfAtwwhairIeY ALgL2Cc.E k 8ABldlY dryiKgohhtSso TrveMsmeQrQv5ezdI.c e 2M1aldgeb 3weiStRho PIlnMfritn5iBtxeF xCxaNlwc0uRlZukss.B Worksheet by Kuta Software LLC  Kuta Software - Infinite Calculus Name___________________________________ Derivatives of Inverse Functions Date________________ Period____ For each problem, find ( f )' ( x) by direct computation. −1 1) f ( x) = −3 x + 3 2) f ( x) = −2 x + 3 ( f −1 )' ( x) = − 1 ( f −1 )' ( x) = − 1 3 2 1 For each problem, find ( f )' ( x) by using the theorem ( f −1)' ( x) = −1 f '( f ( x) ) −1 3) f ( x) = −5 x + 1 4) f ( x) = −2 x + 2 ( f −1 )' ( x) = − 1 ( f −1 )' ( x) = − 1 5 2 5) f ( x) = −2 x − 3 6) f ( x) = −4 x 3 − 4 ( f −1 )' ( x) = − 2 x ( f −1 )' ( x) = − 1 2 2 3 12 ⋅ ( −x − 4 4 ) For each problem, find ( f −1 )' ( x) by using the formula dy = 1 −1 , where y = f ( x) dx dx dy 7) f ( x) = x 7 + x − 3 8) f ( x) = 3 x 5 + 2 x + 5 1 1 ( f −1 )' ( x) = ( f −1 )' ( x) = 7 y6 + 1 15 y 4 + 2 Create your own worksheets like this one with Infinite Calculus. Free trial available at KutaSoftware.com ©7 z240Q1g3s 9K8uXtpa1 tSooIfrtPwNanrYes 5LSL2Cx.G X FAulhlS qrtiEgWh3tPs1 6reeuswe3rJvKeEdX.9 L ZMka7dJeh jwVihtshM 2IYn2fci1neiltpeZ JCiaVlyc0uvl7utst.t Worksheet by Kuta Software LLC