Question

Please explain to me where I want wrong when I tried to differentiate this function.

The function f(x) = xsin(3/x)+34

This is what I did to differentiate this function.

I first used the product rule on xsin(3/x) and I got xcos(3/x)+sin(3/x) as my result. Then after I did this, I used the chain rule to derive the inside of sin(3/x) which is 3/x and the derivative of that is -3/x^2. I then multiplied -3/x^2 to the entire thing I got above when I did the product rule (xcos(3/x)+sin(3/x) thus I got a derivative that ended up looking like this:

(-3/x^2)(xcos(3/x)+sin(3/x))

Answer 1

It shouldn't be multiplied to the entire thing. Just the \(x\cos(3/x)\) part.

Answer 2

Yeah but why? I looked up the derivative of wolfram alpha and saw that, but I want to know why you only multiply the -3/x^2 part to xcos(3/x)

Answer 3

on* wolfram alpha.

Answer 4

When you apply product rule to \(x\sin(3/x)\), we get \((x)^{\prime} \sin(3/x) + x(\sin(3/x))^{\prime} = \sin(3/x) + x(\cos(3/x))\cdot(3/x)^{\prime}\)

Answer 5

ohhh

Answer 6

Took me a while but I think I get it now

Answer 7

I'm going to print screen this so I can stare at your explanation and think about it longer, but I think I sort of get it. But if I stare at it longer it'll absorb into me more.

Answer 8

Okay I just redid the entire problem, differentiated it and got the correct derivative. Thanks I'm going to close this question now.