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.

LC
Answered by Laurence C. Maths tutor

3864 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve y = 2x^3 -ax^2 +8x+2 passes through the point B where x = 4. Given that B is a stationary point of the curve, find the value of the constant a.


Find the area bounded by the curve y=(sin(x))^2 and the x-axis, between the points x=0 and x=pi/2


Solve simultaneously: x + y + 3 = 0 and y = 2x^2 +3x - 1


Solve the following equation by completing the square: x^2 + 6x + 3 = 0.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences