How to solve the equation with square roots

[a1dogtraining]

Homework Statement

I am having trouble to find out what rule to use when solving this equation:
y=5x^2 square root of (2x^3)/15x^7 square root x

How do you right square roots on the keyboard. As you can see I am quit new to this forum

Homework Equations

I have tried to use the chain rule and the quotiant rule. But when I use a different rule I get a different answer.

The Attempt at a Solution

 

[qntty]

Is this the correct equation? (you can see the markup by quoting me)

$$y=5x^2 \sqrt{\frac{2x^3}{15x^7}\sqrt{x}}$$

 

[a1dogtraining]

No
I think it is $$y=5x^2 {sqrt{2x^3}}\15x^7{sqrt{x}}$$

 

[a1dogtraining]

This is what I mean sorry for that

$$y=5x^2\sqrt{2x^3}{frac{15x^7}\sqrt{x}} tex][/QUOTE]$$

 

[qntty]

$$y=5x^2\sqrt{2x^3}{\frac{15x^7}{\sqrt{x}}$$

You can differentiate x to a fractional powers the same way you can differentiate x to an integral power. Try simplifying it first.

 

[a1dogtraining]

Thanks anyway I cann't get the question right. The 5x^2 and sqrt(2x^3) are on the top
and 15x^7 and sqrt(x) are on the bottom. let's try that.

 

[HallsofIvy]

So
$$\frac{5x^2\sqrt{2x^3}}{15x^7\sqrt{x}}$$?
As qntty suggested, you can write the square root as a fractional power: $\sqrt{x}= x^{1/2}$.

Your expression is
$$\frac{5\sqrt{2}x^2x^{3/2}}{15x^7x^{1/2}}= \frac{5\sqrt{2}x^{2+3/2}}{15x^{7+ 1/2}}= \frac{5\sqrt{2}x^{7/2}}{15x^{15/2}}$$
$$= \frac{\sqrt{2}}{3}x^{7/2}x^{-15/2}= \frac{\sqrt{2}}{3}x^{-4}$$
That should be easy to differentiate.

 

[a1dogtraining]

Thank you very much. Can you just tell me what rule you used, so I can apply it to other equations.

 

[HallsofIvy]

I used a number of "rules". I used the fact that $\sqrt{x}= x^{1/2}$, I used the laws of exponents to reduce the problem to a single power of x, and I used the power rule to differentiate.