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If y = 5x^3 - 2x^2 + 2, what is dy/dx?

Differentiation can be done term-by-term, so we can treat the 5x 3 , -2x 2 and 2 separately. We can also 'take out' the coefficients: to differentiate 5x 3 , for example, differentiate x 3 first and then mul...
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Answered by Alex K. • Maths tutor
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Explain the different types of wave.

There are two different types of wave: longitudinal and transverse . When you hear the word "wave" you are probably thinking of a transverse wave. Imagine you are floating in the sea. The waves of ...
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Answered by Harry C. • Physics tutor
5151 Views

Rationalise the complex fraction: (8 + 6i)/(6 - 2i)

The problem with this fraction is the "i" on the denominator, it is not rational. To rationalise this fraction we use the complex conjugate . This sounds more complicated than it is. If a + ib is a...
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Answered by Harry C. • Maths tutor
10911 Views

How do I evaluate something like 3070^2-3069^2?

This looks pretty daunting, but the key to this sort of a problem, which has come up a couple of times in previous PAT tests, is to recognise that this expression is actually the difference of two squares. I...
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Answered by Sam C. • PAT tutor
3731 Views

Find the maximum or minimum value of the function: y = 6x^2 + 4x + 2

The easiest way to solve this problem is by using differentiation . dy/dx = (6x^2 + 4x + 2)/dx dy/dx = 6 2 x^1 + 4 1 x^0 + 0 dy/dx = 12x + 4 When you set the derivative equal to zero you find a point on the ...
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Answered by Harry C. • Maths tutor
11637 Views