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The curve C has equation ye^(-2x) = 2x + y^2. Find dy/dx in terms of x and y.

The curve's equation is presented as an implicit function. Therefore we must use implicit differentiation to solve this problem. To do this, we differentiate both sides of the equation with respect to x, app...
GW
Answered by Georgia W. • Maths tutor
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Let f(x) = x^3 -2x^2-29x-42. a)Show (x+2) is a factor b)Factorise f(x) completely

a) To show (x+2) is a factor, we want to show f(-2)=0. So (-2)^3-2(-2)^2 -29(-2)-42=-8-8+58-42=0 b) Divide x^3 -2x^2-29x-42 by x+2 to get x^2-4x-21 which we factorise to get (x+3)(x-7). Hence f(x)=(x+2)(x+3)...
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Let y = x^x. Find dy/dx.

This question is suited to A2 maths students, particularly those who are doing further maths and may be looking for a challenge. In one question it tests the students ability to use implicit differentiation,...
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Answered by James G. • Maths tutor
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Express as a single logarithm 2 loga 6 loga 3 [2 marks]

loga12 explantion:from simples rules of logs
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How do you know if a function is odd or even?

For this I would use the whiteboard to draw an even function (i.e cos(x)) and show that if f(x) is even then f(x) = f(-x). I would also show that the function would be symmetrical about the y axis. For an od...
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