Quotient Rule

Front

What is the Quotient Rule in algebra?

Back

The Quotient Rule states that if you have a function that is the quotient of two other functions, the derivative of that function is given by: (f/g)' = (f'g - fg') / g².

Front

Simplify: x^10 ÷ x^2

Back

x^8

Front

If a^m ÷ a^n = a^(m-n), what is the result of a^15 ÷ a^8?

Back

a^7

Front

What happens when you divide a number by itself?

Back

The result is 1, as long as the number is not zero.

Front

Simplify: g^25 ÷ g^25

Back

1

Front

What is the result of x^n ÷ x^n?

Back

1, for any non-zero x.

Front

If f(x) = x^4 and g(x) = x^2, what is the derivative of f/g using the Quotient Rule?

Back

(4x^3 * x^2 - x^4 * 2x) / (x^2)^2 = (4x^5 - 2x^5) / x^4 = 2x.

Front

Simplify: 4p^3 ÷ p^2

Back

4p.

Front

What is the general form of the Quotient Rule?

Back

(f/g)' = (f'g - fg') / g².

Front

Evaluate: a^8b^13 ÷ a^6b^5

Back

a^2b^8.