I need help in Calculus (Need Consensus Fast)

I’m taking Calc1 over the summer which, as a 5-credit class, is particularly brutal. I’m in class 14 hours/week and doing at least twice that in homework plus a husband and kids. Let’s not talk about how insane I am, please.

Here’s the issue: I got an 82% on my first test. My second, 65% (I’ve had straight As thus far, so this is killing me). The prof allows us to “fix” one test for half of the remaining points so if I get everything correct on this fix, I can bring it up to an 82, which is huge.

I’ve finished every other error but, I’m stuck on one problem and I need some help. It’s regarding the chain rule of derivatives. Here is the problem:

Let f, g and h be differentiable functions. Find:

[f ° g (x) + x^3h^2(x)]

My answer is currently this:

[fʹg(x) * gʹ(x)] + [3x^2h^2(x) * x^32h(x) * hʹ(x)]

Is that even close to correct? Please help!

At the risk of running afoul of the “no help on homework” rule: yes, it looks correct (assuming I understand your notation correctly).

There’s a “no homework” rule? Well, shit. Sorry mods. Feel free to close this if I’ve violated it. I apologize.

There’s one mistake I see. I’ll just point out that you should be using the product rule on x[sup]3[/sup]h[sup]2/sup and you’ve made a mistake in doing so.

I’m pretty sure just asking for help (as opposed to trying to just get answers) isn’t against the rule.

And I think there’s one typo in your posted answer but otherwise I get the same thing.


{fʹg(x) * gʹ(x)}+ {3x[sup]2[/sup]h[sup]2/sup + x[sup]3[/sup]2h(x) * hʹ(x)}

Thanks for the assist on formatting, too. That was one of the other problems I missed, I was using implicit differentiation and totally forgot something like 3xy means the product rule. I made a lot of stupid, elementary mistakes (bangs head on desk).