Limits
lim x→3 (x + 21)
24
y=2x^2+2x+31
4x+2
∫ 9 dx
9x + C
1 + tan^2(θ)
sec^2(θ)
ln(e) = ?
1
lim x→5 (8x^2 + 7)/ (3x-4)
207/11
(3x-1)(4x+3)
24x+5
∫3x^6−2x^2+3x−9dx
(3x^7/7)-(2x^3/3)+(3x^2/2)-9x+C
What is the chain rule?
f' (g(x)) g'(x)
What is the derivative of tan(x)
sec^2(x)
lim x→4 (5x^4 - 6x^2 - 420)/(x-4)
2555
(x^4+2x^3)/x^2
2x+2
∫ 16x^3+6x^2−22x+4dx
4x^4+2x^3-11x^2+4x+C
d/dx (lnx) = ?
1/x
What is the 2nd derivative of any line segment?
0
lim x→5+ (x+21)/ sqrt(x)
26(sqrt5)/5
y=(7x^3-4x^2+7)^(1/4)
(21x^2-8x)/4(7x^3-4x^2+7)^(3/4)
∫ 8+csc(θ)[sin(θ)+sin(θ)]dθ
10θ + C
If f is continues and different on (a, b) then
f(b)-f(a)/b-a = f'(c)
What is the Quotient Rule?
(g(x) * f'(x) - f(x)) / g^2(x)
lim x→2+ |2x-1|/(3x^2-x)
3/10
y= e^x(x^2-6)
2xe^x+e^xx^2-2e^x
∫ 7e^x+14−2/7xdx
7e^x+14x-2/7*ln(|x|)+C
What is the Rolle's Theorem?
If function f is continuous on [a, b] and differentiable on (a, b) then derivative of f = 0
Find the derivative
y = cos(3x)^-1/2
y' = -sin(3x)/cos(3x)^1/2