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Given y = ln((2x+3)/(7x^3 +1)). Find dy/dx

y = ln(2x+3 / 7x^3 +1) d/dx(2x+3 / 7x^3 + 1) by quotient rule which is(v.du/dx - u.dv/dx) / v^2 where u=2x+3 and v=7x^3 +1 gives (-27x^3 -63x^2 +2) / (7x^3 +1)^2 so d/dx(ln(2x+3 / 7x^3 +1) = ( (-27x^3 -63x^2...
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Answered by Samuel B. • Maths tutor
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What is meant by the term amphoteric? and give an example of a reaction using NaOH that could be used to distinguish between a solution of amphoteric AlCl3 and non-amphoteric MgCl2.

The phrase amphoteric describes a compound that reacts with both acids and bases. NaOH can react with both AlCl 3 and MgCl 2 to give a white precipitate but the addition of excess NaOH causes the amphoteric ...
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Answered by Lois L. • Chemistry tutor
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Is First Past the Post the best electoral system for general elections to the UK Parliament?

Electoral systems can produce significantly different results to each other, and the chosen system prioritizes certain aspects of governance over others. Majoritarian systems (such as FPP or AV) often produc...
TP
Answered by Tom P. • Politics tutor
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Given the function y=(x+1)(x-2)^2 find i) dy/dx ii) Stationary points and determine their nature

Here we have a function made from the product of two functions, so we canuse the product differenciation rule. y=uv => dy/dx=udv/dx + vdu/dx Therefore dy/dy=(x-2)^2 + 2(x-2)(x+1) Stationary points occur w...
RB
Answered by Russell B. • Maths tutor
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How do I begin tackling an unseen passage of Latin for translation into English?

Here's part of a passage taken from an OCR sample language paper: tum magna turba civium ad templum convenit atque ianuam lapidibus obstruxit ne Pausanias exire posset . deinde tectum deleverunt quod speraba...
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Answered by Ho Ting C. • Latin tutor
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