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Write tan(3x) in terms of tan(x). Hence show that the roots of t^3 - 3t^2 - 3t + 1 = 0 are tan(pi/12), tan(5pi/12) and tan(3pi/4)

The first part is relatively simple. If we write tan(3x) as tan(2x+x) we can use addition formulae to give: tan(2x+x)= (tan(2x)+tan(x))/(1-tan(2x)tan(x)) tan(2x) = 2tan(x)/(1-tan^2(x)) Substituing this in an...
DG
Answered by Daniel G. • Maths tutor
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differentiate y = (4-x)^2

This is a basic example of a very important result: the chain rule. The difficulty of this sort of example is that we have a "function of a function". That is, we have the function '4-x' and then w...
BB
Answered by Ben B. • Maths tutor
8763 Views

Differentiate y=e^(x^2+2x)

For this question the chain rule should be used, the chain rule is that dy/du*du/dx=dy/dx. If we say u=(x 2 +2x) and therefore y=e u Then du/dx=2x+2 and dy/du=e u. Then dy/du*du/dx= (2x+2)e u , then we can s...
DF
Answered by Duncan F. • Maths tutor
15478 Views

if y = (e^x)^7 find dy/dx

To solve the the problem we need to recognize what type of differentiation technique we shall be employing y = (e x ) 7 the x unction which we are diferentiating is a power of an exponential function therefo...
GI
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What is the difference between an election and a referendum? (5 marks)

In 5 mark questions, you only need to make 3 points. However, below are all the points that you could make, some with examples. Elections are held at specific intervals. In the UK this is every 5 years. Refe...
RP
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