Question

Below are eight functions. Find the first derivative of each. Space is provided.  Use good dark ink if you are returning this by a scanned version.  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 difficulty (more or less) increases from (a-h).  Be sure to show intermediate work.  Check the scoring rubric to see how the points are awarded.  For example, the first derivative of the function: Y=(2x+3)² is dY/dX=2(2X+3)*(2)

  

Although this can be simplified to: dY/dX=8X+12

please do not simplify your answer.  I can better diagnose your differentiation difficulties.  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.  

a) J=2K² +4K³-3 d) Y=16-4X^1/2+6X^-1/2

            dJ/dK =                                                                       dY/dX =

b) V=Q² -2Q+3Q³ e) T=-2R^-1+7R^-3-48+R²

            dV/dQ=                                                                       dT/dR=                                                

c) D=10-6S² +3S^4/3 f) Q=25-3S²+5S^-3

            dD/dS =                                                                      dQ/dS=

g) B=3Q³*(2Q-3Q²⁾

            dB/dQ =

h) Z=20P^1/4(30P^2/5)

            dZ/dP =