General Contents

Power Rule, Higher Order Derivative, Implicit Higher Order Derivative, Product Rule , Chain Rule , Quotient Rule , Absolute Value , Implicit , Implicit Higher Order , Logarithmic Differentiation Contents: Differentiation

Power

Simple power
Constant * power
Sum of powers
Sum of C * powers
Fractional power > 1
Fractional power 0<p<1
Negative power
Negative fractional power
Sum of two radicals:

General Contents

Higher Order Derivative

Second der: multinomial F'' for
Second der: Quartic:
Second der: Product of simple linear factors:
Second der: Product of general linear factors:
Second der: Product:
Second der: Quotient:
Second der: Radical:
Second derivative: Implicit:

General Contents

Product

Product of linear factors

Polynomial * polynomial

Plus and minus powers

Constant over a power

x times a radical of a power

Product of 2 radicals of a powers:

General Contents

Chain Rule

Linear raised to a power:

Quantity raised to a positive power

Quantity raised to a negative power

Derivative of a product of powers of linear factors:
Derivative of a product of powers, one negative:
Derivative of a product of powers, both negative:
Linear plus reciprocal to a fractional power: Find

for

Explicit chain rule: 2 quadratics: Find

for

,

Explicit chain rule: quadratic and a linear: Find

for

,

Explicit chain rule: quadratic and radicals: Find

for

,

Explicit chain rule: cubic and reciprocal: Find

for

,

Chain Rule: Root of a quadratic: Find

for

Chain Rule: Product of quadratic, root of quadratic:

for

General Contents

;

Quotient

Derivative of a quotient of linear factors

Derivative of a quotient of linear to a quadratic:

Derivative of a quotient of quadratic to a linear:

Derivative of the (ratio of linears) to a power:

Derivative of the quotient of quadratics

Derivative of a cubic over a quadratic

Derivative of x over a radical of a power:
Derivative of the quotient of 2 radicals of powers:

General Contents

Absolute Value

Derivative of Abs(Linear) Derivative of absolute value of a linear

Derivative of absolute value of a linear

Derivative of Abs(Quadratic) Derivative of absolute value of a quadratic

Derivative of absolute value of a quadratic

General Contents

Implicit

Implicit differentiation:

Implicit differentiation:

Implicit differentiation:

Implicit Differentiation: Product of x and y:

.
Implicit Differentiation: Power of y and the product of x and y:

.
Implicit Differentiation: Radicals:

.
Implicit Differentiation: Multinomial:

.
Implicit Differentiation: Quotient:

.
Implicit Differentiation: Radicals:

.
Implicit Differentiation: sin and cos:

.
Implicit Differentiation: xy and tan:

Implicit Differentiation:

:

Implicit Differentiation: Second derivative:

General Contents

Logarithmic Differentiation

Product of power and radical: Logarithmic differentiation of a power times a radical problem
Ratio of radicals:
Powers over a radical:
Fractional power, cosine, radical: $Logarithmic differentiation of a fractioal power, cosine, and radical example$

General Contents