Basic Differentiation Problem

[jpnov]

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

 

[jpnov]

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:

 

[lookagain]

jpnov,

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

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

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

The derivative of the first term is its coefficient.

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

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

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

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

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


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

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

4) Also, \(\displaystyle \frac{5}{2}\) immediately to the left of \(\displaystyle 5\) 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 \(\displaystyle \frac{5}{2}(5u)^\frac{-1}{2}.\)


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

 

[mmm4444bot]

Try this.

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

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.