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What are the derivatives of inverse functions?

For example, for the function y = f(x), the inverse is x = f^-1(y). The derivative with respect to x is calculated using the chain rule, where the derivative of the inverse function over dy times dy/dx becomes the derivative of the inverse function over dy times df/dy. When evaluated, the derivative of the inverse function over dy equals one over the derivative of the original function. For example, the derivative of the inverse function of sin(x) is equal to 1/sqrt(1 - x^2).

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How do you find the domain of a rational function?

Determine which values for x generate a zero in the denominatorThe denominator of a rational expression cannot equal zero. In a simple rational expression, such as 3/x, the only value for x that is not allowed is x = 0, so the domain is expressed as "all x not equal to zero." If there is no x in the denominator, the domain is unrestricted, or "all x."Solve for x by setting the expression equal to zeroIf the denominator is a polynomial, the restricted values for x can be found by setting the denominator equal to zero and solving for x. For example, consider the rational expression 1/x^2 - 4. If..

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What is the "median" in math?

When given a set with an even number of terms, the median is found by averaging the two middle numbers. For example, in the set of numbers 10, 11, 13, 15, 16 and 23, the median is 14, because 14 is halfway between 13 and 15. Before finding the median of a set of numbers, the numbers must be put in order from smallest to largest.

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What are some sources for GCF calculators?

CalculatorSoup is an online calculator resource that features calculators for a number subjects and uses, including algebra, chemistry, statistics and finance. The GCF calculator website provides the calculator, as well as information on how to use factoring and prime factorization to find the greatest common factor or denominator.\nMathsIsFun.com is a mathematics learning resource website that covers kindergarten through 12th grade math curriculum. Mathematicians and math teachers maintain the website, and at least three qualified people review each page. The GCF calculator can find the great..

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How do you measure a curve?

Determine diameterUse a straightedge tool to extend a line from either edge of the curve towards the center. Where these two lines meet is the radius of the circle. Multiply the radius by 2 to get the diameter.Find the angle of the arcCenter a protractor in the middle of the circle so that the zero edge overlays the diameter line. Align the rotating edge of the protractor with the top of the curve. This is the angle of the curve.Solve a formulaMultiply the diameter by pi, and then multiply the solution by the angle. The result is the length of the curve.

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What is expanded form in mathematics?

The decimal system is the most commonly used number system in mathematics. All numbers can be denoted as a power of 10 by using a combination of the whole number 0 and the first nine integers, which are 1, 2, 3, 4, 5, 6, 7, 8 and 9. These numerical characters are also called numerals or digits.A place value pertains to the numerical equivalent of a digit based on where it is positioned in a number. For example, the number 14,382 has a 1 in the ten-thousands' place, a 4 in the thousands' place, a 3 in the hundreds' place, an 8 in the tens' place and a 2 in the digits' p..

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What is the prime factorization of 85?

The simplest prime factorization method is to divide a number by its lowest prime factor and continue doing so to the result until only prime numbers remain. The number smallest prime factor of 85 is 5, which yields 17 when 85 is divided by 5. Because 17 is also a prime number, the final prime factorization of 85 is equal to 5 x 17.

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What is a datum line?

In general, a datum line is a tool used by engineers to ensure the accuracy of measurements. Engineers use the datum line as a horizontal base line to exactly measure various heights. Datum lines are valuable in the development of railway plans, as well as other complex engineering drawings. These lines are critical to guaranteeing measurement precision and avoiding errors from the start of a project.

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What are relatively prime numbers?

For example, 20 and 9 are relatively prime because the only number they can both be evenly divided by is 1 (in other words, 1 is their greatest common factor). On the other hand, 21 and 9 are not relatively prime because you can divide both numbers by 3.\nAs another example, -12 and -13 are relatively prime as the only numbers they can both be evenly divided by are 1 and -1 (having two divisors still makes the two numbers relatively prime). But -15 and -5 can be divided by 5, 3, -5 and -3, and so are not relatively prime.\nThe concept of relatively prime numbers turns up in other number theory..

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What are the characteristics of a good questionnaire?

Technical terms should be avoided in most questionnaires. Questions should not contain words that are not clearly understood. A questionnaire should not contain leading, embarrassing, sensitive or hypothetical questions, and the questions should not contain double negatives. Questions should be presented in a psychologically organized order and should be capable of having a specific answer. The language used should be simple and easily understood.

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