Derivatives and understanding which formula to use.

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kidmo87

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Hello everyone. My teacher listed several problems and siad to find the derivatives. My problem is understand what formula to use. Wheather is power rule, product rule, quotient rule. Rules like that.

f(x)= 3x-1
 x^2+2 Quotient Rule?

f'(x)= (x^2+2) d/dx [3x-1]-3x-1 d/dx [x^2+2]
(x^2+2)^2

f'(x)= (x^2+2)(3)-3x-1(x)
(x^2+2)^2

f'(x)= 3x^2 +6 -3x^2 -x
(x^2+2)^2

f'(x)= -x+6
 (x^2+2)^2 Is this correct. If not, can someone explain to me my errors, thanks.
 
f(x) = g(x)/h(x) -- Quotient rule? Division is in there. Are you sure?

f(x) = g(x)*[h(x)]^(-1) - Multiplication rule?

They are the same.

More important than knowing what formula to use is to use one correctly.
 
I thought the quotient rule was

d/dx [f(x)-g(x)]

=g(x)f'(x)-f(x)g'x)
[g(x)]^2
 
Why would you use a quotient rule for a subtraction? You know "quotient" implies "division," right?
 
your right, i should of put perenthses on there to then multiply by -1. Honestly i really feel like i need help with this. because its 3x-1/xsquared+2, doesnt that imply division? If you know any sites i could learn this kind of concept from, of how to understand which formula to approach this with, or in general of how to understand derivatives and know how to solve them? It would be greatly appreciated. Its really bothering me that i cant comprehend derivatives, and im eager to learn. thanks.
 
kidmo87 said:
f(x)= 3x-1
x^2+2

f'(x)= (x^2+2) d/dx [3x-1] - (3x-1) d/dx [x^2+2]
(x^2+2)^2

f'(x)= (x^2+2)(3) - (3x-1)(2x)
(x^2+2)^2

f'(x)= 3x^2 + 6 - (6x^2-2x)
(x^2+2)^2

can someone explain to me my errors
Click to expand...

Error shown in red. (The derivative of x^2+2 is 2x.)

Now simplify.


PS: After you simplify, you could also factor -1 out of the numerator.
 
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kidmo87 said:
Honestly i really feel like i need help with this. because its (3x-1)/(xsquared+2), doesnt that imply division?
Click to expand...

I feel like you would benefit from proofreading your posts before submission. (This thread contains a number of typographical errors, missing grouping symbols, confusing formatting, and such.) It's difficult to tutor by texting when significant time needs to be invested deciphering or clarifying the poster's intent while simultaneously discussing presentation.

Here's a basic pointer for readability and for avoiding confusion: don't type English words on the same line as equations or algebraic expressions.

There is a [Preview] button to the right of the [Submit] button; you may use it to see how your typing will appear and to check for errors.

Otherwise, you seem to be doing fine mathematically. You correctly chose to use the Quotient Rule, and you only made one mistake (so far).
 
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Untitled.pngOk. Thanks a lot. Ill try to make it more easier to read and understand. Thanks for the pointers.

I have another question about a different problem. Right now i just want to know if im correct by having to use the chain rule.
 

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Please begin a new thread for each new exercise (or topic of discussion).

Thank you. :cool:
 
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