Product/Quotient/Chain
what is the derivative of 5x^7+ x^5 +3/4 x^4 + 2x +8
35x^6 + 5x^4 +3x^3 + 2
what is the derivative of cot(x)?
-csc^2 (x)
what is the integral of 4xsin(2x^2)
-cos(2x^2) + C
what is the integral of 2/ (1+4x^2)
arctan(2x) +C
what is the integral of xlnx?
1/2 x^2 * lnx + 1/4 x^2 + C
what is the third derivative of 9x^4
216x
what is the derivative of a^x
a^x lna
what is the integral of tan(3x)
1/3 ln|sec3x| + C or -1/3 ln|cos3x| + C
what is the integral of (3x^2) / (x^3 +5)
ln|x^3 +5| + C
what is the integral of x^2 * cos(5x) ?
1/5(x^2 sin(5x)) + 1/25(2xcos(5x)) - 1/125(2sin(5x)) + C
what is quotient rule?
f'g- fg' / g^2
what is the derivative of sinxcosx
cos^2 (x) - sin^2 (x)
3 conditions for f(x) to be differentiable
1. f(x) must be cont.
2. f(x) cannot have a vertical tangent on the interval
3. f(x) cannot have a sharp turn (cusp)
what is the integral of 1 / (3x-1)^5
-1/ [12(3x-1)^4] + C
what is the integral of (5x-13) / (x-3)(x-2)
2 ln|x-3| + 3 ln|x-2| + C
what is the derivative of sin(3x^2) * 12x
72x^2 cos(3x^2) + 12sin(3x^2)
what is the derivative of arcsinx
1 / (√1-x^2)
what is the integral of (3e^t)/ (√1-e^2t) ?
3arcsin(e^t) + C
what is the integral of sec(2x) ?
1/2 ln|sec2x + tan2x| + C
what is the integral of x12^x
[12^x (xln12 -1)] / (ln12)^2 + C
what is the derivative of (x^3 lnx) / (x^2 +1)
[(3x^2 lnx +x^2) (x^2 +1) - 2x(x^3 lnx)] /
(x^2 +1)^2
what is the derivative of sin^3 (4x) * 9tan^2(2x)
3sin^2(4x)cos(4x)4(9tan^2(2x)) + 2sin^3(4x)18tan(2x)sec^2(2x)
What are the limit definitions of a derivative? (name at least one)
or lim x->a f(x)-f(a) / x-a
what is the integral of x^3 / (√x^4 + 9)
(√x^4 + 9)/ 2 + C
what is the integral of e^3x * cos (4x)
(e^3x)/25 * (3cos(4x)+ 4sin(4x)) + C