Is there a limit to how many derivative rules you can do within another rule?

[omgwtfitsp]

Like for this question. y = sqrt ( 5x - sqrt ( x^2 + 3 ) ) - this question is a square root within another square root.

So I rearranged it like this:

y = ( 5x - ( x^2 + 3 )^1/2 ) ^1/2

dy/dx = 1/2 ( 5x - ( x^2 + 3 )^1/2 ) ^ -1/2 x ( 5x - 1/2 ( x^2 + 3 )^ -1/2 )

I got up to there, but now should I continue the line and also multiply by (2x) because that's the derivative of the ( x^2 + 3 )? Or does it just stop where I did? Do you always continue to do the derivative until there is no more?

 

[SammyS]

Like for this question. y = sqrt ( 5x - sqrt ( x^2 + 3 ) ) - this question is a square root within another square root.

So I rearranged it like this:

y = ( 5x - ( x^2 + 3 )^1/2 ) ^1/2

dy/dx = 1/2 ( 5x - ( x^2 + 3 )^1/2 ) ^ -1/2 x ( 5x - 1/2 ( x^2 + 3 )^ -1/2 )

I got up to there, but now should I continue the line and also multiply by (2x) because that's the derivative of the ( x^2 + 3 )? Or does it just stop where I did? Do you always continue to do the derivative until there is no more?

Of course it continues, because you haven't finished taking the derivative of ( x² + 3 )^1/2.

Also, ( 5x - 1/2 ( x² + 3 )^-1/2 ) should be ( 5 - 1/2 ( x² + 3 )^-1/2 ) . --- The derivative of 5x is 5 .

It's probably not good to use "x" for a multiplication symbol in the same expression in which "x" is used as a variable.

This https://www.physicsforums.com/blog.php?b=347" has some useful symbols such as: " · " .