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What is the derrivative (dy/dx) of the equation 2 = cos 4x - cos 2y in terms of x and y?

A common C4 question where the student would need to use implicit differentiation to obtain an equation with the derrivative in it. 0 = -4sin4x + 2(dy/dx)sin2y. Then all that is required is rearranging the e...
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Answered by Arsh Y. • Maths tutor
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Find the set of values for which: x^2 - 3x - 18 > 0

Factorise the equation to find the critical values: x^2 - 3x - 18 > 0 (x-6)(x+3) > 0 Critical values:x - 6 = 0x = 6 x + 3 = 0x = -3 Draw a graph where a parabola (shape of a quadratic equation) interse...
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A cubic polynomial has the form p(z)=z^3+bz^2+cz+d, z is Complex and b, c, d are Real. Given that a solution of p(z)=0 is z1=3-2i and that p(-2)=0, find the values of b, c and d.

I will explain this choice of question and demonstrate my approach of showing the most forward way to solve this in the interview.
Answered by • Maths tutor
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Differentiate f = ln(x^2 + 1) / (x ^ 2 + 1).

We'll apply the quotient rule using "u = ln(x 2 + 1)" and "v = x 2 + 1". First we'll need to calculate u' and v'.Using normal differentiation rules, we can see "v' = 2x". Now th...
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Answered by William P. • Maths tutor
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given that y = 1 when x = π, find y in terms of x for the differential equation, dy/dx = xycos(x)

y -1 dy = xcos(x) dx∫y -1 dy = ∫xcos(x) dx ln(y) = ∫xcos(x) dx [using integration by parts to integrate the right hand side] therefore, ln(y) = xsin(x) - ∫sin(x) dxln(y) = xsin(x) + cos(x) + cat y = 1, x = π...
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Answered by Abhiparth S. • Maths tutor
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