# Thread: Find y in terms of x

1. ## Find y in terms of x

Hey,

Could anyone help me with this calculus question?

Find y in terms of x

dy/dx = √x+5 / √x

2. Originally Posted by Oasis1993
Hey,

Could anyone help me with this calculus question?

Find y in terms of x

dy/dx = √x+5/ √x

$\frac{dy}{dx} = \sqrt{x} + \frac{5}{\sqrt{x}}$

$dy = \left( \sqrt{x} + \frac{5}{\sqrt{x}}\right) dx$

$\int y = \int \left( \sqrt{x} + \frac{5}{\sqrt{x}}\right) dx$

$y = \frac{2}{3}(x)^{\frac{3}{2}} + 2(5 \sqrt{x})$

3. Originally Posted by Amer
$\frac{dy}{dx} = \sqrt{x} + \frac{5}{\sqrt{x}}$

$dy = \left( \sqrt{x} + \frac{5}{\sqrt{x}}\right) dx$

$\int y = \int \left( \sqrt{x} + \frac{5}{\sqrt{x}}\right) dx$

$y = \frac{2}{3}(x)^{\frac{3}{2}} + 2(5 \sqrt{x})$
can you relate?

Thank you.

4. Originally Posted by Oasis1993
can you relate?

Thank you.
yeah I forgot to add the constant but

$\frac{dy}{dx} = \frac{\sqrt{x}+5}{\sqrt{x}}$ not

$\frac{dy}{dx} = \sqrt{x} + \frac{5}{\sqrt{x}}$

I solved the second one the first is the same , you should just integrate $1 + \frac{5}{\sqrt{x}}$ instead of $\sqrt{x} + \frac{5}{\sqrt{x}}$

that's your fault you should put bracket like this dy/dx = (sqrt(x) + 5)/sqrt(x)

5. Originally Posted by Amer
yeah I forgot to add the constant but

$\frac{dy}{dx} = \frac{\sqrt{x}+5}{\sqrt{x}}$ not

$\frac{dy}{dx} = \sqrt{x} + \frac{5}{\sqrt{x}}$

I solved the second one the first is the same , you should just integrate $1 + \frac{5}{\sqrt{x}}$ instead of $\sqrt{x} + \frac{5}{\sqrt{x}}$

that's your fault you should put bracket like this dy/dx = (sqrt(x) + 5)/sqrt(x)
Sorry I am new to this forum. I cant use the tools properly.
Could you integrate that for me?
Thank you very much for your help.

6. Originally Posted by Oasis1993
Sorry I am new to this forum. I cant use the tools properly.
Could you integrate that for me?
Thank you very much for your help.

you should know how to integrate it , I integrate the hard part $\frac{5}{\sqrt{x}}$ you just have to integrate $1$ if you can't integrate this it is a big problem you should learn it .

7. $\frac{dy}{dx} = \frac{\sqrt{x}+5}{\sqrt{x}}$

$\int dy= \int \left( \frac{\sqrt{x}+5}{\sqrt{x}}\right) dx$

$y = \int \left(1 + \frac{5}{\sqrt{x}}\right) dx$

$y = x + \frac{5\sqrt{x}}{\frac{1}{2}} + c$

$y = x + 10\sqrt{x} + c$