Search our library of Further Mathematics questions

Top answers

Further Mathematics

All levels

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...

Answered by Mitchell B. • Further Mathematics tutor

1805 Views

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 = mA...

Answered by Oliver K. • Further Mathematics tutor

1956 Views

(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 = k² - 8k* - 18q² i. Plug k into w to give: z = (q + 3i)²- 8*(q - 3i) - 18q² i. k means the compliment of k which just means that the ...

Answered by Emma M. • Further Mathematics tutor

2302 Views

The complex number -2sqrt(2) + 2sqrt(6)I can be expressed in the form rexp(iTheta), where r>0 and -pi < theta <= pi. By using the form rexp(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' ...

Answered by Tajmeet G. • Further Mathematics tutor

2493 Views