You made a mistake on the second last line.
Hello
I have a function:
If I differentiate using the quotient rule, then:
let u = e^x and let v = x
But could I not express as a product ie
And then use the product rule,
Which is a different result! Why so? Or have I done it wrong?
Ah I squared top and bottom rather than multiply by x. I assumed squaring top and bottom would work.
I worked it out with a real example:
incorrect square method:
WRONG!
proper way - multiply top and bottom by 4
or (0.6875) CORRECT!
Well, I have learnt something. Thank you.
Mistakes are the gems of learning. Whenever you make a mistake, assuming the stakes are low such as in a classroom and not as in building a bridge, rejoice that you found it! Then hammer away at that mistake until you know exactly what you did wrong, and have come up with a method for avoiding that mistake in the future.