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How do you differentiate a^x?

The quick answer is that d/dx a^x = ln(a) * a^x. But why? Well, let's go through the steps so we can understand why the formula works. Firstly, a^x can be written as (e^(ln(a)))^x because e^(ln(z)) = z as th...
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Answered by Kian M. • Maths tutor
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Can the creation of a labour union actually cause a loss of employment?

In some circumstances, yes. The introduction of a labour union that fights to gain higher wages by using group bargaining tactics could create a minimum wage floor above the pre-existing market equilibrium w...
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Answered by Conor A. • Economics tutor
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How effective is Aristotle's Virtue Ethics as a practical ethical system in the modern day?

No other ethical theories take into account a person's character quite as much as Virtue Ethics. Actions should be pursued in moderation by not acting with excess or deficiency. Aristotle called this the gol...
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Differentiate the function: y = sin(x^2)*ln(5x)

We are tasked with differentiating y = sin(x 2 ) ln(5x) This function is actually a product of the functions: sin(x 2 ) and ln(5x) Therefore the product rule will be required. First let's calculate the deriv...
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Answered by Thomas C. • Maths tutor
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A 0.20 kg mass is whirled round in a vertical circle on the end of a light string of length 0.90 m. At the top point of the circle the speed of the mass is 8.2 m/s. What is the tension in the string at this point?

A diagram would be very beneficial for this problem. We can draw a free body force diagram of the mass. At the top of the circle the two forces acting on it are its weight and tension from the string. Both a...
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Answered by Thomas C. • Physics tutor
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