Question

What is Power rule, Product rule, Quotient rule and Chain rule? Detail please

Answer 1

The power rule states that when raising a term with an exponent to another power, you multiply the exponents. The product rule states that when multiplying two terms with exponents, you add the exponents. The quotient rule states that when dividing two terms with exponents, you subtract the exponents.

Step-by-step explanation:

Power rule: When raising a term with an exponent to another power, multiply the exponents together. For example, (xᵃ)ᵇ = x^(a*b).

Product rule: When multiplying two terms with exponents, add the exponents together. For example, (xᵃ)*(xᵇ) = x⁽ᵃ⁺ᵇ⁾.

Quotient rule: When dividing two terms with exponents, subtract the exponent of the denominator from the exponent of the numerator. For example, (xᵃ)/(xᵇ) = x⁽ᵃ⁻ᵇ⁾.

Chain rule: In calculus, the chain rule allows you to find the derivative of composite functions. It states that the derivative of a composite function is equal to the derivative of the outer function times the derivative of the inner function. For example, if y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

Answer 2

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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