Sorry about my handwriting
The last step I just used the distributive property
Hello, I'm having some brain freeze on finding the derivative for this problem.
First, I changed the denominator to , and then used the Product Rule.
That left me with:
This is where I'm getting brain frozen. I checked the back off the book it says the answer is: .
I'm not sure where the value of came from. I see parts of the Chain Rule, but the 128.772 has me dumbfounded. If there's a coefficient in front of what happens when taking the derivative of ?
If you feel insistent about the Product rule:
I thought this might not be clear enough and I was going to make some changes but it's late and I have to sleep so bye for now
Hello, AZach!
The derivative of: .
. . . . . . . . . . .is: .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
Unless you are very good at handling negative exponents,
. . I do not recommend switching to the Product Rule.
First off, thanks for the thorough responses, Daigo and Soroban. For this quoted part, I think this is where one of my main problems has been. I knew the derivative of was itself, so I ignorantly assumed that a coefficient in front of the 'x' variable wouldn't alter that. Looking at this from a function point of view, is and both considered inside functions of ?
Absolutely - it's a glass-onion / russian doll situation!
Just in case a picture helps...
... where (key in spoiler) ...
Spoiler:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
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