Question

derivative of x^sqrtx?

Answer 1

so we are finding the derivative of:
\[x*\sqrt{x}\]

Answer 2

Are you familiar with logarithmic differentiation ethayer? :)

Answer 3

\[\large x^{\sqrt x}\]

Answer 4

ah

Answer 5

zepdrix, is that taking the natural log of both sides?

Answer 6

Yes, it will allow us to get the variable OUT of the exponent (using properties of logs)! :) Making the problem doable (with the product rule).

Answer 7

TuringTest please explain it.

Answer 8

@zepdrix seems to have a handle on it

Answer 9

\[\large y=x^{\sqrt x}\]take the natural log of both sides

Answer 10

Just post a response if you get stuck ethayer.
Try to remember your rules of logs, how you can move that exponent OUT of the log! :D

Answer 11

lny = sqrtx * lnx?

Answer 12

now differentiate implicitly

Answer 13

what does that exactly mean? take both sides to the power of e?

Answer 14

no, take the derivative on both sides with respect to x

Answer 15

for \(\frac d{dx}\ln y\) you will need the chain rule

Answer 16

dy/y = [1/2sqrt(x)*ln(x)] + [sqrtx * 1/x]?

Answer 17

it's better to write y', not dy (dy is a differential, which is a different thing) but aside from that, yes

Answer 18

then i just multiply by the original y?

Answer 19

yes