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=6**Q*^{4}*-**2**Q*^{2}*+18Q*
f)
*K=4M**-**3**M*^{2}*+5**M*^{-3}*-**7**M*^{3}

dD/dQ = dK/dM =

b)
*T=2**Q ^{2}*

dT/dQ= dU/dV =

c) P = 25 – Q^{3} + 5Q^{-5} – 7Q^{5}
h)
*W=3**X*^{-1/4}*+2**X*^{2}*-**4**X*^{1/3}

dP/dQ = dW/dX =

d) R = 11 + 7S^{-3} + 5S^{2} +
11S^{-2 }
i)
*Y=**Z*^{2}*(3**Z*^{2}*-**2**Z*^{3}*)*

^{ }
dR/dS =
dY/dZ =

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

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

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