Math Question

[Mozart]

A few years without it and I've forgotten everything.

I am trying to take the derivative of

4*Square root of (x + 4/x)

or just

Dx 4(x + 4/x)^1/2

shouldn't it just be
1/2*4 (x + 4/x)^-1/2 * Dx (x + 4/x)

2/(x + 4/x) ^1/2 * (1 + Dx 4x^-1)

2/(x + 4/x) ^1/2 * (1 - 4x^-2)

2 * (1 - 4x^-2) / (x + 4/x) ^1/2

2 -8x^-2 / (x + 4/x) ^1/2

something like this?

[Opus106]

An odd thing to find in a music forum, but, yes, that's right. Although, I'd leave it at the pen-ultimate step, as it looks much better.

[Coopmv]

A few years without it and I've forgotten everything.

I am trying to take the derivative of

4*Square root of (x + 4/x)

or just

Dx 4(x + 4/x)^1/2

shouldn't it just be
1/2*4 (x + 4/x)^-1/2 * Dx (x + 4/x)

2/(x + 4/x) ^1/2 * (1 + Dx 4x^-1)

2/(x + 4/x) ^1/2 * (1 - 4x^-2)

2 * (1 - 4x^-2) / (x + 4/x) ^1/2

2 -8x^-2 / (x + 4/x) ^1/2

something like this?

The answer is: