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What is the derivative of ln(2x)?

In order to prove the derivation of ln(ax), substitution and various derivatives need to be taken. For the sake of proof, let a = 1. Therefore, ln(ax) can be rewritten as ln(x). It is also necessary to use the function e^x, which is the inverse function of ln(x). According to the laws of inverse functions, when inverse functions are applied to one another, they cancel one another out. Therefore, e^ln(x) is equal to x. Since this function is somewhat long, it can be simplified by setting y equal to ln(x). This allows e^ln(x) to be rewritten as e^y. This function can now be differentiated. Takin..

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What is the difference between a square and rhombus?

All the angles of a square are equal. The rhombus has two sets of opposite internal angles with the same measurement.\nBoth the square and rhombus are quadrilaterals and parallelograms—they have four sides, and their opposite sides are parallel. The two shapes have all sides equal. Every square, by definition, is considered a rhombus, but a rhombus is not always a square.

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Where I can find a free online algebra solver?

WolframAlpha can take any algebraic equation with one or more unknown variables and process it. Users need only input the formula; they do not need to download special software. Aside from answers to equations, the site also plots the equation on a graph. Users who pay for a subscription can get access to step-by-step solutions and an algebraic problem generator to help increase their proficiency in algebra.

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How do you calculate circumference?

The circumference is the distance around a circle. The Greek letter pi is an irrational number beginning with 3.14. If the diameter of a circle is 1, then the circumference of a circle is pi, or 3.14. The equation is typically written as C = pi * d = 2 pi * r, where C is the circumference, d is the diameter and r is the radius. The circumference differs from the perimeter in that a perimeter is used to measure geometric figures with straight lines, whereas the circumference measures a continuously differentiable curve.

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How do you factor perfect square trinomials?

Determine if the first term has a coefficientx^2 + 10x + 25\nIf the first term in the trinomial has no coefficient, then the first term in the binomial is simply x.\n\n9x^2 - 8x + 16\nIf the first term in the trinomial has a coefficient and it is a perfect square, then the first term is the root of the coefficient and x. In the above case, it would be 3x.\n\nDetermine the root of the last coefficientx^2 + 10x + 25\nThe last term is a perfect square, and in this case, its root is 5.\n\n9x^2 - 8x + 16\nThe last term is a perfect square, and in this case, its root is 4.Verify the middle coefficie..

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What is a pie graph used for?

Each section in a pie graph is a different color so that viewers can easily see how the sections compare. Pie charts are often used to explain budgets, taxation issues or other financial matters.\nFor example, if someone wants to make a pie graph of the family budget, the total amount of money earned is represented by the chart as a whole. The pieces of the chart represent the different ways the family's earnings are spent. Different pieces could represent their taxes, grocery bills, car payments, savings contributions or any other categories that they wish to include in the budget. Using..

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What is the definition of "y-intercept"?

Using the slope intercept form of an equation, expressed as y = mx + b, the variable b is equal to the y-intercept, and the variable m is equal to the slope. When x is zero, the value of mx is also zero, resulting in y = b. When graphed, the y-intercept can be found at the point where the graph of the function crosses over the x-axis.

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What are all the factors of 36?

Factors are the positive, non-zero whole numbers which, when divided into the number in question, result in a number with no remainder. In the case of 36, for example: 36 ÷ 2 = 8.\nA whole number greater than 1 which has only two factors (itself and 1) is termed a prime number. Examples of prime numbers include 3, 5, 7 and 11.\nFactoring can also be applied to algebraic expressions. One example of the usefulness of an algebraic factor lies in the polynomial equation x^2 - x - 2 = 0. The factors of x^2 - x - 2 are (x-2) and (x+1), resulting in the simpler equations x-2=0 and x+1=0, yielding ..

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What is the definition of "volume" in math terms?

The formula for volume varies by shape. For a square or rectangle, volume is measured by multiplying length times width times height. An object that is 1 foot long by 3 feet wide by 5 feet deep has a volume of 15 cubic feet. The volume of a pyramid equals 1/3 times the length of the base times the height.

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What does the kinetic theory of matter state?

The differences among objects in the three states of matter are described and explained through the kinetic theory. The kinetic theory breaks down the fundamental differences among solids, liquids and gases based on their arrangement and patterns of movements. Solid particles are generally heavier and exist in compact clusters. They are arranged in predictable patterns, and have limited movement, which is confined primarily to vibrations around a local position. Like solids, liquid elements exist in clusters, and stick close together in given spaces. Liquids, however, unlike solids, have a ran..

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