definition

definition form

Geometric meaning (insert diagram, tangent slope, normal equation of the curve at point M)

Differentiability and continuity (theorem)

common law

Special form [Algebraic interpretation of the invariant form of first-order differential form: dy=f’(u)du]

definition

n-order derivatives of common elementary functions

definition

form

If it is differentiable, it must be differentiable; if it is differentiable, it must be differentiable (necessary and sufficient conditions)

The derivative is also called the derivative

The geometric meaning of differential: the change of the ordinate of the tangent line of the curve at point M

basic formula

Differential Rules of Four Arithmetic Operations

Differentiation Rules for Composite Functions

theorem

theorem

Two important corollaries

Applicable situation: Type 0/0 undetermined

theorem

Applicable situations: ∞/∞ type unfinished formula

theorem

∞-∞ type is converted into type 0/0

The 0·∞ type is first converted into fractional form

After the power index function is first converted into vlnu with the help of the exponential function, it is all 0·∞ type unfinished formula.

Monotonicity of Derivatives

Extreme value and maximum value of function

The concave and convex points and inflection points of functions

rate of change and relative rate of change

marginal cost