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Find the derivative of the arctangent of x function

y = arctan(x)Start by taking the tangent of both sides:tan(y) = xTake the derivative of each side with respect to x, using implicit differentiation/the chain rule for the LHS, then rearrange to make dy/dx th...
MB
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MEI (OCR) M4 June 2006 Q3

The question may be seen here: https://pmt.physicsandmathstutor.com/download/Maths/A-level/M4/Papers-OCR-MEI/Combined%20QP%20-%20M4%20OCR%20MEI.pdf i) Let A = 4E-4 W, B=1E4 m/s^2 s.t. P = m A V*(B+V^2).Recog...
OK
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(FP1) Given k = q + 3i and z = w^2 - 8w* - 18q^2 i, and if w is purely imaginary, show that there is only one possible non-zero value of z

k = q + 3i and z = k 2 - 8k* - 18q 2 i. Plug k into w to give: z = (q + 3i) 2 - 8*(q - 3i) - 18 q 2 i. k means the compliment of k which just means that the sign before the imaginary value is switched to neg...
EM
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The complex number -2sqrt(2) + 2sqrt(6)I can be expressed in the form r*exp(iTheta), where r>0 and -pi < theta <= pi. By using the form r*exp(iTheta) solve the equation z^5 = -2sqrt(2) + 2sqrt(6)i.

Using an argand diagram we can see that this (in fact all) complex numbers create a right angled triangle and using this fact we can find the modulus of this number. The modulus of this number is the 'r' in ...
TG
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Show that G = {1, -1} is a group under multiplication.

We must prove the four axioms of a group are satisfied (i.e Identity, Associativity, Closure, and Invertibility). Identity: The identity element is an element e in G such that e x = x e = x for all x in G. C...
RT
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