Limits
Power Rule
Chain Rule
Derivative
Antiderivative
100
1/9x + 5
lim x → ∞
0
100
Differentiate g(x) = 3x + 5
g'(x)=3
100
y= (2x-5)3
y'= 6(2x-5)2
100
F(x)= (9x6+4x3)3
F'(x)= (216x5+48x2)(9x6+4x3)3
100
f(x) = 6x + 5
F(x)= C+3x2+5x
200
x2 − 8x + 16/x4 − 15x2 − 16
lim x→4
0
200
Differentiate A(s) = − 11s6
A'(s)= 66s-7
200
y= (1+x2)6
y'= 12x(1+x2)5
200
f(x)= 
(7x + 3)
f'(x)= 7/27x + 3
200
f ″(x) = 2x + 6ex
f(x)= 1/3 x^3+6ex+Cx+D
300
3x2 − x + 8/2x2 + 5x − 5
lim x → ∞
3/2
300
Differentiate y = x(x − 14)
y'= 3x-14/2x
300
y= 1/1+x2
y'= -2x(1+x2)2
300
f(x)= cos(x2)
f'(x)= -2xsin(x2)
300
g(t) = 3t
G(t)= 3ln|t|+C
400
(h − 8)2 − 64h
lim h → 0
-16
400
Differentiate F(r) = 6r3
F'(r)= -18/r4
400
f(x)= -3sin(4x2+5)
f'(x)= -24xcos(4x2+5)
400
f(x)= (2x-5)4(x2+x+1)5
f'(x)= 8(2x-5)3(x2+x+1)5+(2x3-3x2-3x-5)4(10x+5)
400
f ″(x) = 12x3 + 36x − 1
f(x)= 3/5 x5+6x3-1/2 x2+Cx+D
500
5x2 + 3/x2 + 2x − 2
lim x → −1
-8/3
500
Differentiate g(t) = 4t-3/8
g'(t)= -3/2t-(11/8)
500
y= cot2(sin(𝜃))
y'= -2(cot(sin(𝜃)))csc2(sin(𝜃))cos(𝜃)
500
F(t)= e7tsin(2t)
F'(t)= 7e7tsin(2t)sin(2t)+14e7tsin(2t)cos(2t)
500
f ″(x) = 8x3 + 5, f(1) = 6, f ′(1) = 4
f(x)= 2/5 x5+5/2 x2-3x+61/10