50KnownTechniques

toc = Differentiation Techniques = (from Maths Methods)

Polynomials
For any term in a polynomial: math \dfrac {d}{dx} \left( ax^n \right) = nax^{n-1} math

Example

The Chain Rule
Use for composite functions: f(g(x)) math \dfrac {dy}{dx} = \dfrac {dy}{du} \times \dfrac {du}{dx} math

Example

The Product Rule
Use when 2 functions are multiplied together math \dfrac{d}{dx} \left( uv \right) = u \times \dfrac {dv}{dx} + v \times \dfrac {du}{dx} math

Example

The Quotient Rule
Use when 2 functions are divided math \dfrac{d}{dx} \left( \dfrac{u}{v} \right) = \dfrac {v \times \dfrac {du}{dx} - u \times \dfrac {dv}{dx}}{v^2} math

Example

**See also** [|www.mathsonline.com.au] Y12Advanced --> Calculus --> Introductory Calculus --> Lesson 3,4,5

Natural Logarithms
math \dfrac {d}{dx} \left( \log_e ax \right) = \dfrac {a}{ax} = \dfrac {1}{x} math

math \dfrac {d}{dx} \left( \log_e g(x) \right) = \dfrac {g'(x)}{g(x)} math
 * Chain Rule Version**

Example

Exponentials
math \dfrac {d}{dx} \left( e^{nx} \right) = ne^{nx} math

math \dfrac {d}{dx} \left( e^{g(x)} \right) = g'(x)e^{g(x)} math
 * Chain Rule Version**

Example

Trig Functions
Derivatives of Trig Functions

Differentiation on the Calculator
Your calculator can do differentiation.
 * diff** is in the ACTION menu, CALCULATION submenu.

Example Enter math \text {diff} \left( (2x^3-3x)^4, x \right) math

OR

You can use the differentiation form, in the **2D** part of the virtual keyboard, select **CALC** on the bottom row.

Example

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