The Student Room Group

HNC Differentiation - On the right lines?

Hi all,

First time looking at differentiation in a long time so jus hoping someone would be able to help me confirm I'm correct or at least on the right lines please?

Scenario: You work as a Test Engineer for a global manufacturer of electrical and mechanical components and systems. Your Line Manager is responsible for delegating to you and your colleagues the testing of theory, principles, and hypotheses from several worldwide company divisions. They have asked you to undertake a series of such evaluations.

Activity Task 1: Differentiate each of the following functions with respect to time and hence determine the ‘rate of change’ for each of the functions when time t, is 2 seconds. Ensure units are given in each case.

i = (3t^2+5t-1)^3

Let u = 3t^2 + 5t - 1
du/dt = 3t^2 + 5t - 1
= 6t+5

i = (u)^3
di/du = 3u^2

di/dt = du/dt * di/du = (6(2)+5) * 3(3(2)^2+5(2)-1)^2
= 17 ∙3(12+10-1)^2
=17∙3(21)^2
=17∙3∙441
=22,491A/s or 22.491 kA/s

Mainly just want to make sure no silly mistakes, the process and notation is ok and the units in the final answer are good too.

Thanks for your help,
Adam
Reply 1
Original post by AdamMc90
Hi all,
First time looking at differentiation in a long time so jus hoping someone would be able to help me confirm I'm correct or at least on the right lines please?
Scenario: You work as a Test Engineer for a global manufacturer of electrical and mechanical components and systems. Your Line Manager is responsible for delegating to you and your colleagues the testing of theory, principles, and hypotheses from several worldwide company divisions. They have asked you to undertake a series of such evaluations.
Activity Task 1: Differentiate each of the following functions with respect to time and hence determine the ‘rate of change’ for each of the functions when time t, is 2 seconds. Ensure units are given in each case.
i = (3t^2+5t-1)^3
Let u = 3t^2 + 5t - 1
du/dt = 3t^2 + 5t - 1
= 6t+5
i = (u)^3
di/du = 3u^2
di/dt = du/dt * di/du = (6(2)+5) * 3(3(2)^2+5(2)-1)^2
= 17 ∙3(12+10-1)^2
=17∙3(21)^2
=17∙3∙441
=22,491A/s or 22.491 kA/s
Mainly just want to make sure no silly mistakes, the process and notation is ok and the units in the final answer are good too.
Thanks for your help,
Adam

Looks great.
Screenshot 2024-05-23 115643.png
Reply 2
Great, thank you so much!

Quick Reply