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Differentiate the function f(x) = 3x^2/sin(2x)

Using the product rule, f=uv, df = (vu'-uv')/v^2. we first set u = 3x^2 and v = sin(2x). u' = 6x, v'=2cos(2x) Therefore, vu' = 6x sin(2x). uv' = 6x^2 cos(2x), v^2 = 4cos^2(2x) Therefore the differential is [...
KS
Answered by Kilian S. • Maths tutor
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Comment on whether an increase in saving will reduce inflation

If there is an increase in saving, then assuming that income stays exactly the same, this will mean that there is a fall in spending as we are saving a higher proportion of our income - or in other words our...
JK
Answered by James K. • Economics tutor
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Solve algebraically the simultaneous equations: x^2+y^2 = 25 and y-3x=13

To answer this question, we need to make y the subject of the second equation. We can do this through simple rearrangement: y-3x=13 so y=13+3x Now that we have y on its own, this means we can substitute for ...
JK
Answered by James K. • Maths tutor
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Differentiate the function f(x)=2xsin3x

Use the product rule: u'v + uv' u = 2x V= sin3x u'= 2 v'= 3cos3x = (2)(sin3x) + (2x)(3cos3x) = 2sin3x + 6xcos3x
TW
Answered by Thomas W. • Maths tutor
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Describe and explain Anselm's Ontological Argument.

The Ontological Argument is one of five classical arguments for the existence of God, using a prior logic (knowledge without experience). It was formulated primarily by St Anselm (1033-1109), defining God as...
LL
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