Solving a differential equation with substitution

[BearY]

This is a small part of a question from the book, so I think the format does not really apply here.

When doing questions for solving differential equation with substitution, I encountered a substitution $y(x)=\frac{1}{v(x)}$. And I am not sure about the calculus in finding $\frac{dy}{dx}$ in terms of $\frac{dv}{dx}$ .

I guess I can post the whole question if the format is really mandatory but this is the only part I can't figure out.

Thanks in advance!

 

[PeroK]

This is a small part of a question from the book, so I think the format does not really apply here.

When doing questions for solving differential equation with substitution, I encountered a substitution $y(x)=\frac{1}{v(x)}$. And I am not sure about the calculus in finding $\frac{dy}{dx}$ in terms of $\frac{dv}{dx}$ .

I guess I can post the whole question if the format is really mandatory but this is the only part I can't figure out.

Thanks in advance!

It's the chain rule. Let $f(x) = 1/x$, then:

$y(x) = f(v(x))$

 

[BearY]

It's the chain rule. Let $f(x) = 1/x$, then:

$y(x) = f(v(x))$

Haha, right. I guess I should stop and get some rest.

 

[Mark44]

I guess I can post the whole question if the format is really mandatory

Yes, it's really mandatory, but I'll let things slide this time.