Derivatives
The derivative of
(x^2+2)^2
4x(x^2+2)
Constant Rule: Derivative of c where c is a constant
0
The anti-derivative of
ex
e^x+C
True or False: Related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known.
True
Point slope form of a line
What is y-y1=m(x-x1) ?
The derivative of
x^{\pi}
\pi x^{\pi-1}
Power rule: Derivative of
x^n
n x^{n-1}
The anti-derivative of
1
x+C
The rate of change is usually with respect to...
Time
A line or curve that a function approaches without actually reaching is this term.
What is an asymptote?
The derivative of
ln(x)
1/x
Product Rule: Derivative of f(x)g(x)
f'(x)g(x)+f(x)g'(x)
The anti-derivative of
Sec2x
\tan(x) + C
Air is being pumped into a spherical balloon at a rate of 6 ft3/min. Find the rate of change of the radius when the radius is 2 ft.
Hint. Use V = 4/3 𝝅r3
3/8𝝅 ft/min or 0.119 ft/min
The branch of mathematics concerned with rates of changes between variables as well as areas under curves that represent functions.
What is Calculus?
The derivative of
\pi^x
\ln(\pi) \cdot \pi^x
Quotient Rule: Derivative of f(x)/g(x)
What is (g(x)f'(x)-f(x)g'(x))/(g(x))2 ?
The anti-derivative of
x
\frac{1}{2} x^2 + C
Given x and y are both differentiable functions of t and y = 3x2, find dy/dt when x = 2 given dx/dt = 4 when x = 2
48
Two ways that a function can be not differentiable.
What are discontinuities and corners?
The derivative of
e^{\sin(x)}
\cos(x) e^{\sin(x)}
Chain Rule: Derivative of f(g(x))
What is f'(g(x))g'(x)?
The anti-derivative of
3(x-152462834756)2
(x-152462834756)^3+C
A ladder 10 ft long rests against a vertical wall. I f the bottom of the ladder slides away from the wall at a rate pf 1 foot per second, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall?
-3/4 ft/sec
Who is Anton?