Derivative Rules
d/dx (e^(4x))
4 e^(4x)
The average rate of change of H(t) between t = 4 and t = 10 can be computed by...
3/2 x^2 + C
d/dx (3 tan x)
3 sec^2 x
If f'(x) < 0, then f(x) is ...
decreasing
(e^(2x) - sin(x))
1/2 e^(2x) + cos(x) + C
d/dx (4/x) =
-4/x^2
if f''(x) > 0, then f'(x) is ...
increasing
d/dx (1/(x^3 + 2x)) =
-1/(x^3 + 2x)^2 * (3x^2 + 2)
The average value of f(x) on [-2, 5] can be computed by...
1/7 * integral of f(x) dx from -2 to 5
(3x^2 + 2x)*(x^3 + x^2 + 1)^5
1/6 (x^3 + x^2 + 1)^6 + C
d/dx (f(2x + 1)) =
f'(2x + 1) * 2
If H''(3) < 0, then a line tangent to H at x = 3 will be above or below the graph of H(x)?
above
g'(x) * sqrt(g(x))