If f (x)=x^n, where n is a natural number, then f′(x)=nx^n-1

If P(x)=f (x)g(x), where f (x) and g(x) are differentiable functions, then

P′(x) =f′(x)g (x) +f (x)g′(x).

moved from an origin over a period of time

• Velocity the rate of change of displacement of an object

with respect to time

• Acceleration the rate of change of velocity with respect

to time

An object is slowing down, at time t if v(t) a(t) <0

The second derivative of a function is determined by differentiating

the first derivative of the function.

For a given position function s(t), its velocity function is v(t), or s′(t),

and its acceleration function is a(t), v′(t), or s″(t).

When v(t) = 0, the object is at rest, or stationary.

Given two differentiable functions g(x) and h(x), the derivative of the

composite function f (x)=g[h(x)] is f′(x)=g′[h(x)] h′(x)

If y=f (u) and u=g(x) are differentiable functions, then dy/dx=dy/du`du/dx

then q(x) can be expressed as q(x)=f (x)[g(x)] ^-1.

Then q′(x)=f (x)(-1)[g(x)]^-2 g′(x)+f′(x)[g(x)]^-1.