Question

Do you find this differentiation approach sane?

http://screencast.com/t/W1bJgZMz

Answer 1

The last derivative you take is wrong.

d/dx (4 + (3x)^1/2) should just be sqrt(3)/(2sqrt(x))

Answer 2

sane? yes .. alot better than "first principles"

Answer 3

its the chain rule that i was trying to describe to you last time :)

Answer 4

So it's 100% correct?

Answer 5

well, the sanity of it is 100% ... the correctness along the way may be suspect

Answer 6

inbefore saying that sanity is a derivate of correctness :D

Answer 7

derivative*

Answer 8

\[let:~\\u=4+(3x)^{1/2}\\u'=\frac{3}{2(3x)^{1/2}}\]
\[(4+(3x)^{1/2})^{1/2}~\to~u^{1/2}\]
\[D_x[u^{1/2}]=\frac{1}{2u^{1/2}}*u'\]
\[\frac{1}{2(4+(3x)^{1/2})}*\frac{3}{2(3x)^{1/2}}\]

Answer 9

its correct?

Answer 10

\[\frac{1}{2(4+(3x))^{1/2}}*\frac{3}{2(3x)^{1/2}}\]
\[\frac{3}{4\sqrt{3x} \sqrt{4+(3x)}}\]

Answer 11

your "since d/dx" step is off

Answer 12

can you spot the error by comparing mine with yours?

Answer 13

yes I spotted it!