Derivative of 5x + (3x + √2x)^½: Step-by-Step Guide

[ussjt]

Question:

Find the derivative of the function: https://webwork2.math.ohio-state.edu/courses/math151wi06sm/tmp/png/Hmwk4/126384/kopko.4-prob16image1.png

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.

 

[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.

 

[krab]

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

 

[ussjt]

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

which brackets?

 

[ussjt]

sorry to bump the topic

but could someone please explain what bracket krab means.

 

[VietDao29]

sorry to bump the topic

but could someone please explain what bracket krab means.

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.

 

[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.

 

[NateTG]

sorry to bump the topic

but could someone please explain what bracket krab means.

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

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

 

[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.

 

[Tom McCurdy]

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

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