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Prove, using the product rule that, the derivative of x^{n} is nx^{n-1} where n is a natural number. What if n is an integer or n is rational?

We know that d / dx (x) = 1. Looking at x^2 as a specific example, and using the product rule, we see that d/dx(x^2) = xd/dx(x) + d/dx(x)x = x + x = 2x. Similarly for x^3, d/dx(x^3) = 3 * x^2 * d/dx(x) = 3 x...
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Answered by Alfred H. • Maths tutor
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With regard to foreign policy, are the powers of the President limited to persuasion?

With regard to foreign policy, the President's powers clearly extend beyond persuasion. Most obviously, the President is commander in chief. This means he is the chief commander of the army, and can order sp...
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The line AB has equation 5x+3y+3=0. The line AB is parallel to the line with equation y=mx+7 . Find the value of m.

Rearrange first equation to show y=-5/3x-1 lines are parallel therefore gradient is the same m=-5/3
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Answered by Isabel C. • Maths tutor
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Explain in terms of bonding and structure the properties of graphite given that it is a good conductor, soft and has a very high melting point

It is a good conductor as there are delocalised electrons. It is soft as the layers are only held together by weak Van der Waals' forces so they can slide over one another. It has a high melting point as you...
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Answered by Isabel C. • Chemistry tutor
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Describe the pathway of oxygen getting from the air into the blood in the human body

diaphragm flattens and the chest wall moves up and out to decrease the pressure in the thorax. Inspiration occurs bringing air from the atmosphere into the mouth/nose and down the trachea, into the bronchi, ...
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Answered by Isabel C. • Biology tutor
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