Below are eight ﬁmctions. Find the ﬁrst derivative of each. Space is provided. All of the

derivatives can be found by using combinations of the constant rule, power function rule and

sum-difference rule. Do not use the product rule. It is not needed. The degree of diﬁculty

(more or less) increases ﬁ‘om (a) to (h). Be sure to show intermediate work. Check the scoring

rubric to see how the points will be awarded. For example, the ﬁrst derivative of the function: Y: (2): + 3)2 is g = 2(2X+ 3)(2)

Although this can be simpliﬁed to: g = 8X +1.2

please do not simplify your answer. [This also avoids more algebraic mistakes on your part.

Hint: To make either (g) or (h) easier, multiply the two parts together ﬁrst, then ﬁnd the

derivative of the resulting product. This avoids the need to use the product rule. Good

Luck! a) Y=GQ3—SQZ+GQ—5 51) T=U5”+2U5”—3U"”

m= new b) Y=10+4X4—3X2 g) I1V=3V‘—45+2V3

W= wig: c) Q=P3’3—P‘3’3+P i) U=5V3+3V‘3—5V3+15

W: wfﬂ= g) z =3W2[2+3W2)

W: h) z = 4X1”(2X— 3X“)

m=