Power Rule|
When raising an exponential expression to a new power multiply the exponents.
For and Example|
Simplify: 7a^4 b^6)2
Solution: Each factor within the parentheses should be raised to the 2nd power.
7a^4 b^6)2 = 7^2(a4)2(b^6)2
You then simplify using the power Rule of Exponents.
7a^4 b^6)2 = 7^2(a4)2(b^6)2 = 49a^8 b^12
The power rule states that this derivative is n times the function raised to the (n-1) the power times the derivative of the function.
Product Rule|
When multiplying exponential expressions that have the same base, add the exponents.
Example:
Multiply: 4x^3 • -6x^2
Solution:
Multiply coefficients: 4 • -6 = -24
Use the product rule to multiply variables.
X^3 • x^2 = x^3 + 2 = x^5
4x^3 • -6x^2 = -24x^5
The power of product rule is a method for simplifying exponents and it states that a term raised to a power is equal to the product of its factors raised to the same power.
The product of two or more numbers is the result of multiplying these numbers.
Quotient Rule|
When dividing exponential expressions that have the same base, subtract the exponents.
Example:
Simplify: 8x^6/2x^3 = 4x^3
Solution:
Divide coefficients:
8 /2 = 4
Use the Quotient rule to divide variables:
X^6/x^3 = x6 - 3 = x^3
8x^6/ 2x^3 = 4x^3
The Quotient of two numbers is the result of the division of the numbers.
Chain Rule|
The general power rule is a special case of the chain rule. It is useful when finding the derivative of a function that is raised to the nth power.
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