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- Calculus
- Limits
- Continuity
- Definition of the Derivative - First Principles
- Basic Differentiation Rules
- More Differentiation Rules
- Implicit Differentiation
- Higher Order Derivatives
- Curve Sketching
- First Derivative Test
- Second Derivative Test
- Derivatives of Trigonometric Functions
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Logarithmic Functions
- Derivatives of Exponential Functions
- Antiderivative
- Indefinite Integral
- Applications of the Indefinite Integral
- The Definite Integral
- Area Under a Curve - Riemann Sums
- Area Under a Curve - Integration
- Area between Two Curves
- Volumes of Revolution
- Logarithmic Integrals
- Exponential Integrals
- Trigonometric Integrals
- Trigonometric Integrals of Other Forms
- More Integration Methods

**CONSTANT FUNCTION RULE **

A **constant function*** *is of the form \( f(x) = b \) where *b *is some real number. The derivative of ALL constant functions is always 0.

Consider \( f(x) = 5 \). We will have that \( f'(x) = 0 \).

*Why is this so? *

Suppose you are driving a car from point A to point B, and the whole time you are driving 40km/h. Your speed does not change, and so the car is going at a **constant **pace. If you were to calculate the *rate of change *of your speed, you would get zero - because there IS no change in your speed!

**POWER RULE **

The

Consider \( f(x) = x^5 \).

\( \Longrightarrow f'(x) = 5x^{5-1} \)

\[ \Longrightarrow f'(x) = 5x^4 \]

**CONSTANT MULTIPLE RULE **

The **constant multiple rule **is a variation of the **power rule**, and applies to functions of the form \( f(x) = cx^n \), where \( c \) is some real number. We have that the derivative of these types of functions is of the form \( f'(x) = (c)(n)x^{n-1} \).

Consider \( f(x) = 4x^6 \).

\( \Longrightarrow f'(x) = (4)(6)x^5 \)

\[ \Longrightarrow f'(x) = 24x^5 \]

**SUM RULE**

The **sum rule **applies to functions with __more than one__ term. To determine the derivative of these functions, we take the derivatives of each of the individual terms. If we have that \( f(x) = g(x) + h(x) \), where \( g(x), h(x) \) are functions, then \( f'(x) = g'(x) + h'(x) \).

Consider \( f(x) = 2x^3 + x^4 \).

\( \Longrightarrow f'(x) = (2)(3)x^2 + 4x^3 \)

\[ \Longrightarrow f'(x) = 6x^2 + 4x^3 \]

- Last Updated: Aug 12, 2022 11:32 AM
- URL: https://libraryguides.centennialcollege.ca/c.php?g=717032
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