Solving for Error in Y: A Math Problem

[lemon]

Homework Statement

$$\[<br /> \[<br /> \begin{array}{l}<br /> {\rm{A quantity Y is given by:}} \\ <br /> Y = \frac{{4a^3 b}}{{\left( {5c^2 \sqrt {\rm{d}} } \right)}} \\ <br /> {\rm{Find the error in Y given the following errors in a, b, c, and d:}} \\ <br /> a \pm 1\% ,{\rm{ }}b \pm 0.5\% ,{\rm{ }}c \pm 2\% ,\,{\rm{ }}d \pm 1.5\% \\ <br /> \end{array}<br /> \]<br /> \$$

Homework Equations

Given above

The Attempt at a Solution

I plugged the numbers into this equation and got 0.1632993162
This is not correct.
I added all the percentage errors together to get 5%. Then asked myself why I did that anyway.
Don't know how to solve this problem. I know how to find percentage errors but these are already given.
please help. Thank you

And also - My LaTex is not working properly - It doesn't recognize the spaces between the words from MathType. Anyone know why?

 

[Stonebridge]

When you combine errors in a formula containing powers with the terms multiplied and divided you add the percentage errors of all the terms, but with the additional factor that if a term is squared the % error is doubled, if it's cubed the % error is 3 times. etc etc.
You can probably find a proof of this online.

 

[lemon]

Thank you