For y=x/(x+4)^0.5, solve dy/dx

As x is present as both numerator and denominator (top & bottom), we're going to use the quotient rule to solve this. The quotient rule is as follows:For y=f(x)/g(x), dy/dx=(f'(x).g(x)-f(x).g'(x))/((g(x))^2) ---See whiteboard for a clearer demonstration
Considering that f'(x).g(x)= The first derivative of f(x) multiplied by g(x). First derivative simply means df(x)/dx i.e just differentiate f(x).
When applied to our question we can see that: f(x)=x so f'(x)=1 and g(x)=(x+4)^0.5 so g'(x)=0.5(x+4)^-0.5 following the chain rule.
We can now substitute these terms into the quotient rule so that dy/dx=((x+4)^0.5 -0.5x(x+4)^-0.5)/(x+4)
This can be further simplified by multiplying all terms by (x+4)^-0.5 to get dy/dx=(x+4-0.5x)/(x+4)^1.5=(0.5x+4)/((x+4)^1.5)

TM
Answered by Thomas M. Maths tutor

3106 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

f(x) = (4x + 1)/(x - 2) with x > 2. Find a value for 'x' such that f'(x) (first derivative of f(x) with respect to x) is equal to -1.


A cubic curve has equation y x3 3x2 1. (i) Use calculus to find the coordinates of the turning points on this curve. Determine the nature of these turning points.


How come x^2 = 25 has 2 solutions but x=root(25) only has one? Aren't they the same thing?


How should I go about solving a quadratic equation?


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning