Given f(x) = (x^4 - 1) / (x^4 + 1), use the quotient rule to show that f'(x) = nx^3 / (x^4 + 1)^2 where n is an integer to be determined.
QUOTIENT RULE: [u(x) / v(x)]' = [u'(x)v(x) - u(x)v'(x)] / v2We have: u(x) = x4 - 1, hence u'(x) = 4x3v(x) = x4 + 1, hence v'(x) = 4x3So we have: [(4x3)(x4 + 1) - (4x3)(x4 - 1)] / (x4 + 1)2Expanding gives us: [4x7 + 4x3 - 4x7 + 4x3] / (x4 + 1)2Giving us a final answer of: [8x3] / (x4 + 1)2, and hence the integer n = 8
TA
Related Maths A Level answers
All answers ▸How do you differentiate 5x
Ignoring air resistance and assuming gravity to equal 9.81. If a ball of mass 1kg is dropped from a height of 100m, calculate it's final velocity before it hits the ground.
Where does the circle (x-6)^2+(y-7)^2=4 intersect with y=x+3
Find dy/dx for y=x^2 * sin(x)