Basic Differentiation Problem

jpnov

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Sep 28, 2010
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screenshot20101010at158.png


I'm really not sure where I went wrong. I used the chain rule (which isn't covered until a later section...). I tried simplifying, my answer is just not being accepted.

Thanks,
Jonathan
 
O god... it's sqrt7, not sqrt(7u)
-_______________________-

I used up all but one of my submissions trying it thinking it was sqrt7u. is my answer to the problem right? before i submit it:

screenshot20101010at321.png
 
jpnov said:

jpnov,

because at that time you were not doing the chain rule, then rewrite it as:

g(u)=(7)u+5(u)=\displaystyle g(u) = (\sqrt{7})u +\sqrt{5}(\sqrt{u}) =

g(u)=(7)u+(5)u12\displaystyle g(u) = (\sqrt{7})u + (\sqrt{5})u^{\frac {1}{2}}

The derivative of the first term is its coefficient.

g(u)=7+12(5)u12\displaystyle g'(u) = \sqrt{7} + \frac{1}{2}(\sqrt{5})u^{\frac{-1}{2}}

g(u)=7+52u12\displaystyle g'(u) = \sqrt{7} + \frac{\sqrt{5}}{2u^{\frac{1}{2}}}

\(\displaystyle g'(u) = \sqrt{7} + \frac{\sqrt{5}}{2\sqrt{u}}}\)

g(u)=7+125u\displaystyle g'(u) = \sqrt{7} + \frac{1}{2}\sqrt{\frac{5}{u}}

g(u)=7+5u2u\displaystyle g'(u) = \sqrt{7} + \frac{\sqrt{5u}}{2u}


Note: \(\displaystyle \frac{5}{2}5u^{\frac{-1}{2}\) is not correct because

1) the "5u"\displaystyle "5u" must have grouping symbols around it,

2) you won't leave the answer with a negative fractional exponent.

The function has the variable inside a radical, so the derivative
should have that variable also inside the radical for consistency in forms.

3) The 5\displaystyle \sqrt{5} that would be in the denominator will cancel
out with with the 5\displaystyle 5 in the numerator of your first fraction,
so you would have just one 5\displaystyle 5 showing.

4) Also, 52\displaystyle \frac{5}{2} immediately to the left of 5\displaystyle 5 does not indicate any multiplication,
that being another reason the grouping symbols would be needed to double
as multiplication. It is meaningless. If you typed it correctly as a possible
intermediate step, it may look like 52(5u)12.\displaystyle \frac{5}{2}(5u)^\frac{-1}{2}.


One of the last few forms of my solution will be the desired one by your
instructor and/or textbook.
 


Try this.

g(x)  =  7  +  54u\displaystyle g'(x) \;=\; \sqrt{7} \;+\; \sqrt{\frac{5}{4u}}

If this (or any of lookagain's versions) were to be rejected, the machine-teacher would be wrong.

:!: An explanation (in writing) from the division chair would be called for.

 
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