Miscellaneous
Product + Quotient Rule
Chain and Power Rule
Integrals
More Miscellaneous
100
d/dx 1
0
100
3 - (1/x) f(x) = ------------- x + 5
-3x^2 + 2x + 5 f'(x) = --------------------- (x^2 + 5x)^2
100
y = x^8
y' = 8x^7
100
f(x) = ∫ 5x^3 + 4 dx
F(x) = (5x^4)/4 + 4x
100
f(x) = ∫ ln(x)
F(x) = 1/x
200
d/dx sinx = x(1+tany)
cosx - tany - 1 ------------------- xsec^2y
200
x f(x) = ---------- x^2 +1
1-x^2 f'(x) = -------------- (x^2 +1)^2
200
y = cos(3x)
y' = -3sin(3x)
200
⌠ x f(x) = ⎮−−−−−−− dx ⌡ √(1-x^2)
F(x) = -√(1-x^2)
200
Suppose x and y are both differentiable functions of t and are related by the equation y = x^2 + 3. Find dy/dt when x = 1, given that dx/dt = 2 when x = 1.
dy/dt = 4
300
Determine the dimensions of a rectangular solid (with a square base) of maximum volume if its surface area is 150 square inches.
5 x 5 x 5 inches
300
f(x) = (3x - 2x^2)(5 + 4x)
f'(x) = -24x^2 + 4x + 15
300
cotx f(x) = ------ sinx
-1 - cos^2x f'(x) = ---------------- sin^3x
300
⌠ x^2 f(x) = ⎮−−−−−−−− dx ⌡ √(25-x^2)
F(x) = (25/2)arcsin(x/5) - (1/2)x√(25 - x^2)
300
BONOUS
Yay, you actually get some points! :)
400
An 8 foot tall ladder is leaning against a wall. The top of the ladder is sliding down the wall at a rate of 2ft/sec. How fast is the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4ft away from the wall?
y = 2√3 ft/sec
400
3 - (1/x) f(x) = ------------- x + 5
-3x^2 + 2x + 5 f'(x) = --------------------- (x^2 + 5x)^2
400
f(x) = x^(4/5) - x^(2/3)
4 2 f'(x) = ------------- - -------------- 5x^(1/5) 3x^(1/3)
400
f(x) = ∫ 4 acos(x) dx
F(x) = 4x acos(x) - 4√(1-x^2)
400
When water is drained out of a conical tank, the volume V, the radius r, and the height h of the water level are all functions of time t. Knowing that theses variables are related by the equation: ∏ V = ---- r^2h 3 At what rate is the volume changing?
dV ∏ ----- = ----- (r^2(dh/dt) + 2rh(dr/dt)) dt 3
500
f(x) = ∫ tanx * dx
F(x) = -ln(cosx) + C
500
x^2 + 3 f(x) = --------------------- x^4 - 3x^2 +1
2x (-x^4 -4x^2 + 7) f'(x) = --------------------------- (x^4 - 3x^2 + 1)^2
500
f(x) = 3sec^2(∏x - 1)
6∏sin(∏x-1) f'(x) = ---------------- cos^3(∏x-1)
500
⌠ sec^2(ln(ln(x)) f(x) = ⎮------------------- dx ⌡ ln(x^x)
F(x) = tan(ln(ln(x)))
500
Find the Volume of the Solid Generated of the upper half of the ellipse: 9x^2 + 25y^2 = 225 rotated about y=0
60∏
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