Given y = 4x/(x^2 +5) find dy/dx, writing your answer as a single fraction in its simplest form

This function is fraction so the easiest method is to use the quotient rule (though the product rule can be used). Recall the quotient rule dy/dx = [vu' - uv']/[v^2]Note, u and v refer to the numerator and denominator respectively u' and v' are the first differentials w.r.t x
For this question: u = 4x v = x^2 + 5 hence: u' = 4 v' = 2xApplying the quotient rule: [(x^2 + 5).(4) - (4x).(2x)]/[x^2 + 5]^2Expanding the brackets in the numerator: [4x^2 + 20 - 8x^2]/[x^2 + 5]^2Simplify: dy/dx = [20 -4x^2]/[x^2 + 5]^2No further cancellation or simplification can be done so, the question is finished.