Calc 1 Exam 2

Definition at (derivative) interior point a

Tangent Line definition/formula (point and slope)

One-way Implication

Differentiable at a → continuous at a. The converse is false. A derivative is a finite slope, not merely a connected graph.

Deriv. Rule: (c)’

0

Deriv. Rule: (sin x)’

cosx

Deriv. Rule: (tan x)’

sec²x

Deriv. Rule: (sec x)’

sec x tan x

Deriv. Rule:

Deriv. Rule: (cos x)’

-sinx

Deriv. Rule: (cot x)’

-csc²x

Deriv. Rule: (csc x)’

-csc x cot x

4-Step Trig Derivative Cycle

sin x → cos x → -sin x → -cos x

sin²x + cos²x =

1

Product Rule: (fg)’

f’g + fg’

Quotient Rule: (f/g)’

f’g - fg’ / g²

Chain rule: