- #1
Aftermarth
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Ok I am in my final study for my last exams... and i just want to check with all you guys that i have my calculus right :)
Derviations:
1. Lower the power by one, and times by the new power out in front of the term. Coefficinets drop off, and terms with just x become a new coefficient in the f ' (x) form.
2. e ^ x dervies to:
(f '(x)) e ^ x
3. ln (f(x)) dervies to
[ f '(x)] / [f(x)]
4. Chain rule
( 3x + 4)^5 becomes:
4(3x + 4)^4 x 3
=12(3x + 4)^4
5. Product Rule:
vu' + uv' where v and u are both functions multiplied together
6. Quotient Rule:
(vu' - uv') / (2v)
f ''(x) is simply the derivative of the derivative
Integration:
1. Raise the power by one and mutliply by 1/new power. Add the constant term (c) and any coefficients now add the term x
eg. x^3 + 2x^2 + 4
integrates to:
(1/4)x^4 + (2/3)x^3 + 4x + c
2. f '(x) / f(x) integrates to ln( f(x)) + c
3. e ^ f(x) integrates to (1/ f '(x)) e^(f(x)) +c
4. There are no chain, product or quotient rule to integration
5. Always add the constant term c, and use a given point to work it out :)
i hope u guys can identify any probelms in my working if there are any :)
Aftermarth
Derviations:
1. Lower the power by one, and times by the new power out in front of the term. Coefficinets drop off, and terms with just x become a new coefficient in the f ' (x) form.
2. e ^ x dervies to:
(f '(x)) e ^ x
3. ln (f(x)) dervies to
[ f '(x)] / [f(x)]
4. Chain rule
( 3x + 4)^5 becomes:
4(3x + 4)^4 x 3
=12(3x + 4)^4
5. Product Rule:
vu' + uv' where v and u are both functions multiplied together
6. Quotient Rule:
(vu' - uv') / (2v)
f ''(x) is simply the derivative of the derivative
Integration:
1. Raise the power by one and mutliply by 1/new power. Add the constant term (c) and any coefficients now add the term x
eg. x^3 + 2x^2 + 4
integrates to:
(1/4)x^4 + (2/3)x^3 + 4x + c
2. f '(x) / f(x) integrates to ln( f(x)) + c
3. e ^ f(x) integrates to (1/ f '(x)) e^(f(x)) +c
4. There are no chain, product or quotient rule to integration
5. Always add the constant term c, and use a given point to work it out :)
i hope u guys can identify any probelms in my working if there are any :)
Aftermarth