Question

Ok, so i have to answer Y=Ln2x/sqrtx with respect to x.
My answer was (1/x 3/2)- (1/2x^2/2)ln2x/x.
The correct answer should be (1-1/2ln2x/sqrtx^2. Can anyone help

Answer 1

\[y = \frac{ \ln 2x }{ \sqrt{x}}\] and you want differentiate it wiht respect to x. Right ?

Answer 2

yes

Answer 3

You should get dy/dx = \[\frac{ 1 }{ x ^{3/2}} -\frac{ \ln 2x }{ 2x ^{3/2}}\]

Answer 4

My college tutor says answer should be : (1-1/2ln2x)/sqrtx^2

Answer 5

@harland407 : Your presentation of your problem statement needs attention. Your "Ok, so i have to answer Y=Ln2x/sqrtx with respect to x" should really read "I need to find the derivative of y=Ln2x/sqrtx with respect to x." Accurately communicating ideas in math is as important as being able to do the math itself.

Answer 6

So: You "need to find the derivative of y=Ln2x/sqrtx with respect to x?" You have done enough work to demonstrate your knowledge that this is a quotient function.

1) What is the derivative with respect to x of ln 2x?

2) What is the derivative of Sqrt(x)?

3) Supposing you have the quotient \[\frac{ u }{ v },\] where u and v are separate functions of x. What is the formula for the derivative? (Quotient Rule)

Answer 7

U=ln2x, v = X 1/2.
du/dx = 1/x, dv/dx = 1/2 x -1/2

Answer 8

Being picky with a purpose, I urge you to improve the presentation of your math statements. v = X 1/2 is subject to misinterpretation: \[x(1/2),~x _{1}/2, \]

Answer 9

...and so on. Please use the tools available to you for this purpose; parentheses, the Draw utility or Equation Editor.

All of the following are acceptable:ways in which to present "the square root of x:"\[\sqrt{x},x ^{1/2},x ^{\frac{ 1 }{ 2 }}, or\] x^(1/2). Your choice. But not x 1/2.

Answer 10

Supposing you have x^(1/2) and are to find the derivative. Here's one way of expressing that:

(d/dx) x^(1/2)=(1/2)x^((1/2)-1). Not fancy, and not pretty, but it's accurate.
Alternatively:\[\frac{ d }{ dx }x ^{1/2}=\frac{ 1 }{ 2 }x ^{(\frac{ 1 }{ 2 }-1)}=\frac{ 1 }{ 2 }x ^{\frac{ -1 }{ 2 }}\]

Answer 11

Let's review:

2) What's the derivative of x^(1/2)? Possible answers (all correct) are:\[(1/2)x ^{-1/2}, \frac{ 1 }{ 2 }x ^{\frac{ -1 }{ 2 }},\]

Answer 12

Take your pick.

1) What is the derivative of ln 2x? Your answer, 1/x, is correct.

3) Write out the Quotient Rule:

(d/dx)(u/v) = ?


... and then we can finish solving this problem.

Answer 13

dy/dx = V du/dx - U dv/dx / V^2

Answer 14

I had : x^1/2 (1/x) - Ln2x (1/2 x^-1/2) / x^1/2^2