I’m confused, are you lamenting Calculus in general or that specific problem?

I’m actually a big believer in Calculus. But that problem is just endless symbolic manipulation that has no real value. It’s simply a time-waster.

I think the point of problems like this is to provide repetitive reinforcement of the concepts being taught. Can you identify the rules that must be applied to this problem (chain rule and quotient rule for example) and apply them in the correct order.

The kids are being taught to do this as a triple chain rule-- "(tan(3x^2))^(-1/2)". And the tangent requires them to remember their trig derivative identities. But there is no real-world case for any of this, so it's just abuse.

You want kids to not hate math? Stop making it about pointless symbolic manipulation and actually show them why calculus matters in the real world. Because it's really, really important.

I think this is a false dichotomy. You can demonstrate both the real world application AND provide conceptually rigorous problems to practice the application of theory. If the real world aspect isn't happening then I agree that's a problem, but both perspectives are appropriate.

Right now our daughter's take-away is that math sucks and she's bad at it. But I keep battling through it with her.

Well I wish the best to you both in that journey. I definitely know the struggle of learning math (i changed to major in history just so I didn't have to take more math). As an adult I'm having to relearn math for a practical reason which definitely makes it more interesting.

I've found that it is fun to turn these complicated problems into a game. I understand that there isn't a real world problem that will involve triple chain rule, but I don't think that means there's no value.

I try to look at it as, "okay, what rules do I know and how can I manipulate this thing to leverage those concepts." Almost like a brain teaser.