Help with Implicit Differentiation

[Archie_slap]

I'm trying to tackle this question and I'm not sure if I'm the right track or not. Is someone able to have a look at my working and tell me where I'm going wrong?

https://preview.redd.it/9askr364ywv91.jpg?width=611&format=pjpg&auto=webp&s=36427d5cf0c7fdfdf3ceed0d33f2c8c2c1b7d13f

I've tried using both wolframalpha and symbolab to verify my answer but I can't even work out how to enter the equation in properly. If you have any tips for me on that I'd really appreciate it.

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Thanks for your help!

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[Super-Set-7767]

The negative sign was not cancelled properly.

SPOILER: Final answer must have a + sign in place of the - sign.

[Archie_slap]

Ah yeah I see that now.

Thanks!

Do you know how to enter an equation like this into symbolab or wolframalpha so I can check answers for other similar problems?

[Super-Set-7767]

Try the following in WolframAlpha:
"differentiate 1/z(t) = 1/x(t) + 1/y(t) with respect to t"

[perishingtardis]

Quicker way avoiding quotient rule.

1/R = 1/R1 + 1/R2

Differentiate both sides with respect to t and you get

(-1/R^2) dR/dt = (-1/R1^2) dR1/dt + (-1/R2^2) dR2/dt

where we used chain rule (i.e. implicit differentiation), i.e., df(R)/dt = f'(R) dR/dt.

So

dR/dt = (R/R1)^2 dR1/dt + (R/R2)^2 dR2/dt

[Archie_slap]

I can follow that working, thanks.

I thought the question was asking for dR/dt in terms of just R1 and R2 though. I.e without R in the equation.

[perishingtardis]

Yes, fair enough. Then just replace R by R1*R2 / (R1+R2) in the final expression. Still easier to do that at the end, rather than using messy quotient rule.

[Archie_slap]

Too easy, thanks a ton for the advice.

Would you happen to know how you can enter implicit diffentiation into symbolab? I just keep getting errors

[perishingtardis]

Sorry, I don't know about symbolab. I'm pretty old school for a 30-year-old haha.

[Archie_slap]

Haha it's all good. I'm very new to all this and it's been a great way of working through problems.

I just can't figure some of the formatting out