Question

​​​​​​

Below are ten functions. Find the first derivative of each. 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) to (j). Be sure to show intermediate work. Five points are awarded for correctly developed derivatives. There is no partial credit, because an incorrect derivative is useless.

For example, the first derivative of the function:          is:

The above is satisfactory, although this can be simplified to:

Please do not simplify your answer. This also avoids algebraic mistakes on your part.

HINT: For (i) and also for (j), multiply the two parts together first, then find the derivative of the product.

a) D=6Q⁴-2Q²+18Q f) K=4M-3M²+5M^-3-7M³

            dD/dQ =                                                                      dK/dM =

b) T=2Q²+3Q^-3+Q³   g) U=10V^1/2+5V^-1/3-4V^-3

            dT/dQ=                                                                       dU/dV =

c) P = 25 – Q³ + 5Q^-5 – 7Q⁵                                     h) W=3X^-1/4+2X²-4X^1/3

            dP/dQ =                                                                       dW/dX =

d) R = 11 + 7S^-3 + 5S² + 11S^-2                                                          i) Y=Z²(3Z²-2Z³)

                    dR/dS =                                                                       dY/dZ =

e) J=7-9L^-3+11L^-2-3L² j)   X=(2Y^1/2-4Y)(2Y²)

            dJ/dL =                                                                        dX/dY =

I have already worked these problems but was looking to ensure I did them correctly. If you do not mind showing your work so that if I did one of the problems wrong I can see where and understand how I messed up. Thank you so much.

Answer 1