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Differentiate y=x^x with respect to x.

y=x^x, taking natural log of both sides
ln(y)=ln(x^x), using laws of logs
ln(y)=xln(x), using product rule and implicit differentiation
dy/dx 1/y=ln(x)+1
dy/dx=(ln(x)+1)y
dy/dx=(l...

Answered by • Maths tutor

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Explain the concept of internal economies of scale and the three stages of returns that can occur when firms increase their factors of production? Graphs maybe used in your answer

Internal economies of scale are centred around the relationship of a firm increasing its factors of production ie. its inputs and how this affects the average cost of producing goods. The general concept ...

Answered by Colm K. • Economics tutor

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What would be the impact on the multipler effect given an increase in income tax?

The multipler effect is when an additional increase in aggregate demand can cause a greater final impact on national income (GDP) than the inital size of the injection, with the multipler being a coeffici...

Answered by Daud B. • Economics tutor

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Show that x^2 - 8x +17 <0 for all real values of x

consider the discriminant b²-4ac 8²-4x1x17 64-68=-4 discriminant is below 0, there are no real roots therefore x² - 8x +17 <0

Answered by • Maths tutor

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In a circuit with a thermistor and bulb, what happens to the brightness of the bulb as the temperature increases?

As the temperature increases, the resistance of the thermistor decreases. So the resistance of the whole circuit decreases. Using V=IR, the PD remains constant but resistance has decreased, so current mus...

Answered by • Physics tutor

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