Calc Unit 2 - Derivatives

Derivatives, rates of change, power rule, chain rule, etc.

Average velocity

Average velocity

(Speed 2 - speed 1)/(x2 - x1)

Limit definition of derivative

The limit as h approaches 0 of f(x+h) - f(x), all over h

Limit definition of the derivative of a function f at the point (c, f(c ))

The limit as h approaches 0 of f(c+h) - f(c ), all over h

Alternative definition of the derivative of f at point c

Limit as x approaches c of f(x) - f(c ), all over (x-c)

When is f(x) differentiable at x=c?

Limit as x approaches c from the left of f(x) - f(c ), all over (x-c) is equal to limit as x approaches c from the right of f(x) - f(c ), all over (x-c)

Derivative of sin x

Cos x

Derivative of cos x

-sin x

Derivative of sec x

sec x tan x

Derivative of csc x

-csc x cot x

Derivative of tan x

Sec²x

Derivative of cot x

-csc²x

Product rule: Derivative of (u * v)

u(dv/dx) + v(du/dx). “First dLast + Last dFirst”

Quotient rule