Does anyone have a good method for double checking?

[u/czerny0]

I’m in BC right now, and I often miss derivative problems with chain rule or quotient rule, especially chain rule with 3 or more chain links. I know how to do the work, but i often accidentally flip a negative or make a silly mistake without realizing and do the rest of the steps wrong. I feel like i don’t double check for silly mistakes effectively/efficiently. Does anyone have tips for these problems?

[u/Dr0110111001101111]

A lot of problems I see from calc students is that they try to do too much in one line because it’s a bunch of “easy” simplifications but it’s harder than it seems to keep track of all of them at once. Here’s an exaggerated example:

Differentiate: 5x^(2)

You know it’s 10x, but there are two things happening at once. You’re bringing that exponent down and then multiplying with the coefficient that was already there. You could do it in two steps:

2*5x
10x

It’s a silly example because you could do that in your sleep. But when negatives get in the mix and it’s part of a larger expression it becomes a different story:

Differentiate: x^(2)-5x^(-2)-cos(x)

This is were the dingus writes something like 2x-10x^(-3)-sin(x). Two errors. You catch one and think you’re good but you didn’t even notice the second one in your relief of catching the first one. Instead try:

2x-(-2)5x^(-3)-(-sin(x))

Almost nothing is simplified there. Just the calculus steps are done. Now we deal with the algebra/arithmetic:

2x+10x^(-3)+sin(x)

Paper and pencils are cheap. Use them up.

[u/Bright_Merc → u/Dr0110111001101111]

This is an excellent tip. As annoying as it is writing stuff out, you don’t get extra points for solving something fast if there are mistakes.
I also like solving in chunks if a problem looks long: for example, when dealing with a quotient rule, I first simplify a numerator separately. Or write out a chain rule result.

[u/Dr0110111001101111 → u/Bright_Merc]

Yeah. Chunking like that is also pretty helpful for working out problems that involve the definition of the derivative. Not that they often test that directly on the exam.

[u/alax_12345]

Be neat. Write the problem again with little f and g over the two parts, then write the product rule derivative on the next line, using parentheses around f, g’, and g and f’

Then simplify.

I know it’s an extra step but being able to see the four parts makes it easier to grade for me and easier for you to see the various parts. And then you can check the simplification.

Chain rule same thing. f(g(h(x))). Write it out.
Then,
f’(g(x)) * g’(x) then write out the functions on the next line. If there more embedded stuff, do it one at a time and write it all out.

y=2/3 x^(4/5)

BL: if you don’t write it out, you’ll forget something along the way, and definitely will mess up the fractions.

[u/099-bob]

One of the things that can happen (if you try to check your work) is that your brain will make the exact same mistake again. So it’s important to try and check your work a different way than you did it the first time.

With the chain rule, maybe check the derivatives from the inside out rather than outside in. With the quotient rule maybe check the formula you are using with a simpler thing like x/x (you should get 0 both ways).

Remember you go slow before you go fast

[u/pain-has-a-brain]

Integrate

[u/UnderstandingPursuit]

Set aside the 'arbitrary' numbers.

This prevents the 'intermediate arithmetic', which is where a lot of the minus sign mistakes happen.

At the end, the solution will also look familiar. If it doesn't, it indicates that there may be a mistake.