How do I calculate the rate of change of something for which I don't have an equation?

This kind of question is an application of differentiation. If t represents time, any derivative with respect to t is a rate of change. For example, if h represents the depth of water in a cubicle container, dh/dt is the change in depth over time, or the rate of change of the depth in other words. If the question does not give you an equation that directly relates the thing you want the rate of change of to time, it will often give you an equation that relates a different quantity to time. For example, it might ask you to calculate the rate of change of volume of water in the container, but not give you an equation for volume in terms of time, and so one differentiation won't suffice. I find it really helpful to write out what I'm trying to calculate and how I could do so with the given terms. Let's say we need to calculate the rate of change of volume of water in the container. We are given that the rate of change of depth (dh/dt) is 10m/s, and that the container is a cuboid with dimensions of 50x50xh m. We want dV/dt. We have dh/dt, so if we write this out we know that dV/dt = (dh/dt)(some other derivative). If you treat derivatives as fractions (which you normally can), you can see that in order cancel out dh, the other derivative must be dV/dh. We know that the equation for volume in terms of h for a cuboid of dimensions 50x50xh is simply V=2500h. Differentiate this and you get dV/dh=2500. All that's left to do is to multiply the two derivatives together, so dV/dt=102500 = 25000. So the rate of change of volume is 25000m^3/s.

Answered by Sam E. Maths tutor

15711 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Use logarithms to solve the equation 3^(2x+1) = 4^100


x^3 + 3x^2 + 2x + 12


(a) By using a suitable trigonometrical identity, solve the equation tan(2x-π/6)^2 =11-sec(2x-π/6)giving all values of x in radians to two decimal places in the interval 0<=x <=π .


How do you find the angle between two lines in three dimensional vector space given two points on line 1 and the vector equation of line 2


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences