Derivatives
d/dx(3x^2+4x-7)
6x+4
sin^2x+cos^2x=
1
intdx
x+C
When do you add +C?
When you evaluate an indefinite integral.
lim_(x->oo)1/x
What is 0?
d/dx(cosx)
-sinx
f'(g(x))g'(x)
What is the chain rule?
inte^(2x)dx
e^(2x)/2+C
int_1^4 f'(x)dx
f(4) - f(1)
lim_(x->0)(cosx-1)/x
What is 0?
d/dx(xe^(2x))
e^(2x)+2x*e^(2x)
(g(x)f'(x)-f(x)g'(x))/(g(x))^2
What is quotient rule?
int(1/(1-2x))dx
-1/2*lnabs(1-2x)+C
lim_(x->a)f(x) = f(a)
What is the definition of continuity?
lim_(x->0)sinx/x
What is 1?
d/dx(arctan(3x))
3/(1+9x^2)
f'(x)g(x)+f(x)g'(x)
What is product rule?
inttanxdx
-lnabs(cosx)+C
sin(pi/4)+cos(pi/3)
(1+sqrt2)/2
lim_(x->0)(3x^2-sinx)/(2x^2+x)
What is 3/2?
d/dx(x^2/(ln(x)))
(2x*ln(x)-x)/(ln(x))^2
f'(c)=(f(b)-f(a))/(b-a)
What is the MVT?
int_1^2 2x(x^2+1)^3dx
156
d/dx(int_0^(3x^2)(cos(x^2)))
What is
cos(9x^4)*6x
lim_(h->0)((3+h)^2-9)/h
f'(3)=6