If f(x) = sin(2x)/(x^2) find f'(x)
As f(x) is in the form of u(x)/v(x) we can apply the rule that f'(x) = (u'(x)*v(x) - v'(x)*u(x))/(v(x)2), pulled from the C3 formula booklet.
If u(x) = sin(2x) then u'(x) = 2cos(2x).
If v(x) = x2 then v'(x) = 2x.
Hence, f'(x) = ((2cos(2x)*x2) - (sin(2x)*2x))/(x4)
(Will be easier to explain on a whiteboard w/ standard visualisation of functions)
LR
Related Maths A Level answers
All answers ▸How do I integrate 4x*exp(x^2 - 1) with respect to x?
Use implicit differentiation to find dy/dx of the equation 3y^2 + 2^x + 9xy = sin(y).
Integrate | x^7 (ln x)^2 dx ( | used in place of sigma throughout question)
A curve is defined for x>0 as y = 9 - 6x^2 - 12x^4 . a) Find dy/dx. b) Hence find the coordinates of any stationary points on the curve and classify them.