ITT: Math tricks and shortcuts
You can quickly find the derivative of any power function by adding 1 to the exponent then multiplying the term by the new exponent. For example:
f(x) = 5x^4
f'(x) = (5)(5)x^(4+1)
f'(x) = 25x^5
Sure shaves a lot of time off of differentiating big polynomials and polynoginals.
Seems risky. Does it work every time?
>>8929704
so you are really just multiplying f(x) by the term (5x) in this case?
>>8929704
but that derivative is wrong brainlet
>>8929708
Technically you can factor the constant out of the derivative and distribute it back in later, but in this case it's unnecessary because of order of operations. See "constant multiple rule"
OP check your math...
ITT: OP CAN'T INTO DERIVATIVES... FFS
That bait is sooo hectic bro!
I fully raged! (and saged)
>>8929704
What the fuck?
I feel like this is intentional.
You cannot fail if you don't even try in the first place.
>>8929722
Faggot check your dubs.
>>8929706
f(x) = 7x^3
f(x) = (4)(7)x^(3+1)
f(x) = 28x^4
this will really help me with polys
Jesus Christ I hope you're a troll and not this much of a retarded faggot.
>>8929704
I like this trick a lot. Here's my trick for integrating power functions:
You subtract 1 from the exponent and then divide by the coefficient by the old exponent.
f(x) = 5x^4
F(x) = (5/ 4)(x^4-1)
F(x) = (5/4)x^3
I have a cool trick for differentiating exponential functions
Let's say you have a function b^x
The derivative is always b^x log x.
Works every time and sure beats trying to take the difference quotient of that mess.
>>8929763
Except no, that's the wrong derivative.
>>8929713
>>8929722
>>8929730
>>8929815
>being baited this easily
>>8929760
F(x) = 7x^3
F(x) = (7/3)(x^3-1)
f(x) = (7/3)x^2
wow! I'll be applying this method to predator prey models in no time!