1.
If the two functions f(x) and g(x) are differentiable (i.e. the derivative exist) then the product is differentiable is called the...
Correct Answer
A. Product rule
Explanation
The product rule states that if two functions, f(x) and g(x), are differentiable, then the derivative of their product is equal to the derivative of f(x) times g(x) plus f(x) times the derivative of g(x). This rule is used to find the derivative of a product of functions.
2.
A method of finding the derivative of a function that is the ratio of two differentiable functions is...
Correct Answer
A. Quotient rule
Explanation
The correct answer is the Quotient rule. The Quotient rule is used to find the derivative of a function that is the ratio of two differentiable functions. It states that the derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. This rule is particularly useful when dealing with functions that involve division, as it allows us to find the derivative of the quotient function.
3.
What can be used to find the derivative of a function?
Correct Answer
A. Quotient rule
Explanation
The quotient rule is a formula used to find the derivative of a function that is the quotient of two other functions. It states that the derivative of the quotient of two functions is equal to the denominator multiplied by the derivative of the numerator, minus the numerator multiplied by the derivative of the denominator, all divided by the square of the denominator. This rule is essential in calculus for finding the rate of change of a function and determining critical points. A calculator, angle, or BODMAS (a mnemonic for the order of operations in mathematics) are not directly used for finding derivatives.
4.
The answer after you divide one number by another is the...
Correct Answer
C. Quotient
Explanation
When you divide one number by another, the answer you get is called the quotient. The quotient represents how many times the second number can be divided into the first number evenly. For example, if you divide 10 by 2, the quotient is 5 because 2 can go into 10 five times without any remainder. Therefore, the correct answer is "Quotient."
5.
The product of two or more numbers raised to a power is equal to the product of each number raised to the same power is...
Correct Answer
A. Product rule
Explanation
The product rule states that the product of two or more numbers raised to a power is equal to the product of each number raised to the same power. This means that when multiplying numbers with the same base raised to a power, you can simply add the exponents. For example, (a^m)(a^n) = a^(m+n). Therefore, the correct answer is the product rule.
6.
The number which we divide is called the...
Correct Answer
A. Dividend
Explanation
The number which we divide is called the dividend.
7.
The number by which we divide is called the...
Correct Answer
D. Divisor
Explanation
The number by which we divide is called the divisor.
8.
The number left over after division is called the...
Correct Answer
D. Remainder
Explanation
The number left over after division is called the remainder. This is the amount that remains after dividing one number by another, when the division is not exact. It represents the "leftover" or "extra" amount that cannot be evenly divided.
9.
To divide two exponents with the same base, keep the base and subtract the powers. This is...
Correct Answer
A. Quotient rule
Explanation
The explanation for the given correct answer, "Quotient rule," is that when dividing two exponents with the same base, you can keep the base the same and subtract the powers. This rule is known as the quotient rule in exponentiation.
10.
The quantity produced by the division of two numbers is...
Correct Answer
A. Quotient
Explanation
The quantity produced by the division of two numbers is called the quotient.