Math Subject GRE tricks/formulas/identities

Term
1 / 33
d(aⁿ)
Click the card to flip 👆
Terms in this set (33)
d(aⁿ)
log(a)aⁿdn
d(logn)
dn/n
d(sin(n))
cosndn
d(cos(n))
-sin(n)dn
d(tan(n))
sec²(n)dn
d(cot(n))
-csc²(n)dn
d(sec(n))
sec(n)tan(n)dn
d(csc(n))
-csc(n)cot(n)dn
d(arcsin(n))
dn/√(1 - n²)
darctan(n)
du/(1 + n²)
sin(a + b)sin(a)cos(b) + cos(a)sin(b)cos(a + b)cos(a)cos(b) - sin(a)sin(b)sin(a - b)sin(a)cos(b) - cos(a)sin(b)cos(a- b)cos(a)cos(b) + sin(a)sin(b)cos(2a)1 - 2sin²(a), cos²(a) - sin²(a)sin(2a)2cos(a)sin(a)Choose U for Integration By PartsI LATESecond Derivative Test of f(x,y)Determinant Hessian matrix of f(x,y)Hessian Determinant > 0, fxx(P) < 0Local max @ PHessian determinant > 0 fxx(P) > 0Local min @ PHessian determinant < 0Saddle pointHessian = 0No conclusionGreen's Theorem∫closed curve, Mdx N dy = ∫∫R (Dn/dx - Dm/dy)dAPath Independent Line integralConservative vector field, depends only on endpointsAuxiliary Polynomial with real rootsy = c₁e^m1 + c₂e^m2Auxiliary polynomial with complex rootse^(ax)(c₁cosbx + c₂sinbx)Auxiliary polynomial with identical real rootsy = c₁e^m1 + c₂xe^m2ax²y'' + bxy'+cyFind roots in form ar(r - 1) + br + c, put in form c₁x^r₁ + c₂x^r₂projection of a onto b(BB/BA)BSpherical coordinate xpsinphicosthetaspherical coordinate ypsinphisinthetaspherical coordinate zpcosphiFermat's Little theorema^p modp = a; a^p-1 mod p = 1