Using the product rule, f'(x) = 2x * ln(x) + x.

Using the chain rule, f'(x) = (1/(x^2 + 1)) * (2x) = 2x/(x^2 + 1).

Using the product rule, f'(x) = (x^2)' * e^x + x^2 * (e^x)' = 2x * e^x + x^2 * e^x.

The transitive property does not apply in sports; thus, we cannot conclude the relationship between Player A and Player C.

If A beats B and B beats C, it can be inferred that A is better than C.

Number of attendees from outside = 25% of 800 = 0.25 * 800 = 200.

Number of attendees from urban areas = 800 * (1 - 0.25) = 800 * 0.75 = 600.

Number of non-students = 1,600 * (1 - 0.25) = 1,600 * 0.75 = 1,200.

Number of adults = 70% of 350 = 0.70 * 350 = 245. Number of children = 350 - 245 = 105.

Number of soldiers from country A = 25% of 120 = 0.25 * 120 = 30.

During a phase change, the temperature of a substance remains constant while the substance absorbs or releases heat.

In an isochoric process, the volume of the gas remains constant.

In an isochoric process, the volume of the system remains constant.

In an isothermal process for an ideal gas, the internal energy remains constant because the temperature does not change.

During inhalation, the diaphragm contracts, increasing the volume of the thoracic cavity and decreasing the pressure, allowing air to flow in.

The Industrial Revolution brought about significant changes in urbanization and infrastructure, leading to more organized disaster response mechanisms.

During metaphase, chromosomes align at the metaphase plate, preparing for separation.

Oxygen enters the bloodstream during inhalation when air is drawn into the lungs and diffuses across the alveolar membrane.

During exhalation, the diaphragm relaxes, causing the thoracic cavity to decrease in volume and air to be expelled from the lungs.

Ovulation occurs during the ovulatory phase of the menstrual cycle when an egg is released from the ovary.

The endometrium thickens during the luteal phase of the menstrual cycle in preparation for a potential pregnancy.

The embryo implants into the uterine wall during the blastocyst stage of development.

The correct form is 'Each of the students has completed their assignments.' 'Each' is singular, so it should be followed by 'has'.

The subject 'Each' is singular, so it should be 'has'.

The correct form is 'Either the cat or the dogs are making noise.' The verb agrees with the nearest subject 'dogs', which is plural.

Ethylene is produced in response to low oxygen levels, particularly during stress conditions like flooding.

Let θ = tan^(-1)(1). Then, cos(θ) = 1/√(1 + tan^2(θ)) = 1/√(1 + 1) = 1/√2.

Using the triangle with opposite = 3 and adjacent = 4, hypotenuse = 5. Thus, cos(tan^(-1)(3/4)) = 4/5.

Using the right triangle definition, cos(tan^(-1)(5/12)) = adjacent/hypotenuse = 12/13.

cos^(-1)(0) = π, since cos(π) = 0.