# Where did I go wrong?

1. Feb 7, 2006

### ussjt

Question:

Find the derivative of the function:

My answer:

Can please someone tell me where I messed up.

Edit: i used that chain rule or something like that

So first I changed the equation into [5x+(3x+sqrt(2x))^.5]^.5

then I found the first derivative, so it was .5[5x+(3x+sqrt(2x))^.5]^-.5

Next I did it for 5x and the 1/2 power-> 5+.5(3x+sqrt(2x))^-.5

I did the same for the following 2 steps. I hope that helps.

Last edited: Feb 7, 2006
2. Feb 7, 2006

### Pengwuino

If you can show us what you did step-by-step (i know, that's hard with square roots unfortunately), we can help you determine where you went wrong.

3. Feb 7, 2006

### krab

your brackets are messed up. The last (third) bracketed factor does not multiply everything, just the part that starts with 3x.

4. Feb 7, 2006

### ussjt

which brackets?

5. Feb 8, 2006

### ussjt

sorry to bump the topic

but could someone please explain what bracket krab means.

6. Feb 8, 2006

### VietDao29

It may be quite impossible for us to guess your approach, and thus, we don't know where you went wrong. Now, may I ask you to post step by step solution, so that we can check it for you. :)
You don't have to LaTeX, or use MS Equation Editor, just jot down your steps in a paper, then use a scanner and post it here. :)
You can also learn how to LaTeX. There are three PDFs on the first post of that thread. The thread is a sticky in the Math & Science Tutorials board.

7. Feb 8, 2006

### assyrian_77

He means that the "inner derivatives" do not multiply the entire expression. The last bracket - which by the way is not correct - is not supposed to be multiplied with the entire expression. It has to be inside the second bracket.

EDIT: Explained better hopefully, without giving out too much of the solution.

Last edited: Feb 8, 2006
8. Feb 8, 2006

### NateTG

What is meant is that the grouping (where the parentheses are) is incorrect.

Hint:
$$\frac{d}{dx}\sqrt{3x+\sqrt{2x}} \neq \left(3+\frac{.5}{\sqrt{2x}}\right)*2$$

9. Feb 8, 2006

### krab

The 3rd big bracketed factor has to be INSIDE the bracket just ahead of it. IOW, it does not multiply the 5+ of the second big bracketed factor.

10. Feb 8, 2006

### Tom McCurdy

$$\frac{1}{2}(3x+(2x)^{1/2})^{1/2})^{-1/2}*(5+\frac{1}{2}(3x+(2x)^{1/2})^{-1/2}*(3+\frac{1}{2}(2x)^{-1/2}*2))$$

=

$$\frac{20*\sqrt{x}*\sqrt{\sqrt{x}*(3*\sqrt{x}+\sqrt{2})}+6*\sqrt{x}+\sqrt{2}}{8*\sqrt{x}*\sqrt{\sqrt{x}*(3*\sqrt{x}+\sqrt{2})}*\sqrt{\sqrt{\sqrt{x}*(3*\sqrt{x}+\sqrt{2})}+5*x}}$$

Last edited: Feb 8, 2006
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