03 - Power, Constant, and Sum Rules

1 D M2L0T1g3Y bKbu6tear hSBo0futTwjaZrTeA s VARlilZ OrciVgyh5tXst L EMVaodNeG lwxictDhI AIcnafoi0nliqtxec by Kuta Software LLCKuta Software - Infinite CalculusName_____ Period____Date_____Differentiation - Power, Constant, and Sum Rules Differentiate each function with respect to ) y = 52) f( x) = 5 x183) y = 4 x5 + x4) f( x) = 4 x4 5 x 35) y = 3 x 546) y = 54 x 237) y = 4 x 58) y = 3 x39) y = x 2310) f( x) = 24 x -1- q b2b081L3S cKNuitpax uSWoffitiwHaPrYez 4 QAnl0lK BrOipgohutwsX e tMdaZdSeI CwgiZtlhw NImntfdiMnoiQtweA by Kuta Software LLC 11) y = 23 x4 + 5 x x 312) y = 12 x4 + 3 x 53 + 2 xDifferentiate each function with respect to the given ) y = 3 r5 5 r214) f( s) = 3 s2 4 s415) f( x) = 23 x 32 34 x 3516) h( s) = 2 3 s + 2 5 s Differentiate each function with respect to x.

2 Problems may contain constants a, b, and ) y = 5 c18) y = 4 a x3 a b x3 c-2- l b2M0i1x3o rKkuRtbap TSzoBfxtrwGaxrXeP o 8A4l9lm trOiSgoh9tOsC f cMVamdWeY EwZietshO aILnRfBiunDi9tGel by Kuta Software LLCKuta Software - Infinite CalculusName_____ Period____Date_____Differentiation - Power, Constant, and Sum Rules Differentiate each function with respect to ) y = 5 dy dx = 02) f( x) = 5 x18 f '( x) = 90 x173) y = 4 x5 + x dy dx = 20 x4 + 14) f( x) = 4 x4 5 x 3 f '( x) = 16 x3 55) y = 3 x 54 dy dx = 15 x 1446) y = 54 x 23 dy dx = 56 x 13 = 5 6 x 137) y = 4 x 5 dy dx = 20 x 6 = 20 x68) y = 3 x3 dy dx = 9 x 4 = 9 x49) y = x 23 dy dx = 23 x 13 = 2 3 x 1310) f( x) = 24 x f '( x) = 12 x 34 = 1 2 x 34 -1- z u2y0s1r3L QKQudtKaJ 6 SwoHf0tdwUa8rmec c zAzlFlF Nrdilg0hJtmst l wMmaidPea jwqiXt6he VIAnUfoiBnfimtbeZ by Kuta Software LLC 11) y = 23 x4 + 5 x x 3 dy dx = 83 x3 + 5 + 3 x 4 = 8 x33 + 5 + 3 x412) y = 12 x4 + 3 x 53 + 2 x dy dx = 2 x3 + 5 x 23 + 2 Differentiate each function with respect to the given ) y = 3 r5 5 r2 dy dr = 15 r4 10 r14) f( s) = 3 s2 4 s4 f '( s) = 6 s 3 + 16 s 5 = 6 s3 + 16 s515) f( x) = 23 x 32 34 x 35 f '( x) = x 12 920 x 25 = x 12 9 20 x 2516) h( s) = 2 3 s + 2 5 s h '( s) = 13 s 232 + 15 s 452 = 2 3 s 23 + 2 5 s 45 Differentiate each function with respect to x.

3 Problems may contain constants a, b, and ) y = 5 c dy dx = 018) y = 4 a x3 a b x3 c dy dx = 12 a2 x 3 a 1 3 bc x 3 c 1-2-Create your own worksheets like this one with Infinite Calculus. Free trial available at