# HNC calculus

Hi guys im really struggling with calculus at the moment can someone give me some guidance on where to start with this please i know i need to apply the power rule to this to get the derivative but unsure where to go from here.

Differentiate each of the following current functions with respect to time and hence determine the ‘rate of
change’ for each of the functions when time, t, is 3 seconds.
a) 𝑖 = (3𝑡 + 5)^4
Original post by Jeffers999
Hi guys im really struggling with calculus at the moment can someone give me some guidance on where to start with this please i know i need to apply the power rule to this to get the derivative but unsure where to go from here.

Differentiate each of the following current functions with respect to time and hence determine the ‘rate of
change’ for each of the functions when time, t, is 3 seconds.
a) 𝑖 = (3𝑡 + 5)^4

so to differentiate this we use the chain rule, it is as follows

times by power
times by derivative of bracket
-1 from power

this will give you di/dt and then just plug in t=3
Original post by B7861
so to differentiate this we use the chain rule, it is as follows

times by power
times by derivative of bracket
-1 from power

this will give you di/dt and then just plug in t=3

Ive given this an attempt but still think im on the wrong route
when multiplying the power i get to
12t+5^4 and seem to be stuck again
Original post by Jeffers999
Ive given this an attempt but still think im on the wrong route
when multiplying the power i get to
12t+5^4 and seem to be stuck again

Remember the last step, minus 1 from power which you haven’t done. So it will be (12t+5)^3
Original post by B7861
Remember the last step, minus 1 from power which you haven’t done. So it will be (12t+5)^3

Think ive got there now thankyou after doing that and substituting in t=3
(12(3)+5)^3
41^3
= 68921 does this seem right
yes sound right, btw are you doing A level maths
Original post by Jeffers999
Think ive got there now thankyou after doing that and substituting in t=3
(12(3)+5)^3
41^3
= 68921 does this seem right
Original post by Jeffers999
Think ive got there now thankyou after doing that and substituting in t=3
(12(3)+5)^3
41^3
= 68921 does this seem right

No
Original post by Meltboy7778
No

okay im lost then really unsure where to go after getting
(12t+5)^3
Original post by B7861
yes sound right, btw are you doing A level maths

not sure ive applied this correctly and no im currently studying my HNC/D for electrical engineering and this is my last maths assignment
Original post by Jeffers999
okay im lost then really unsure where to go after getting
(12t+5)^3

What is ((3𝑡 + 5)^3) x 12?
It isn't (12t+5)^3
(edited 1 year ago)
Original post by Meltboy7778
What is (3𝑡 + 5)^3 x 12?
It isn't (12t+5)^3

why does the it all get multiplied by 12 i thought if you apply the power rule the 3t would then become 12t
Original post by Jeffers999
Ive given this an attempt but still think im on the wrong route
when multiplying the power i get to
12t+5^4 and seem to be stuck again

Have you been taught how to use the chain rule? The steps you are attempting to follow do work if applied correctly but without a real understanding of the reasons why.

Following the suggested method here and a different example

if 𝑖 = (4𝑡 + 5)^10

if you first multiply the bracket by the original power you get 10(4𝑡 + 5)^10
if you then also multiply by the differentiated content of the bracket and reduce the power by 1 your result should be
(10)(4)(4𝑡 + 5)^9
d𝑖/dt = 40(4𝑡 + 5)^9
(edited 1 year ago)
This comes down to understanding the chain rule.
If you're going through a worksheet I don't see how you could have got to this point without it being explained.

The way I was taught it, this works because you replace the stuff in the powered bracket with a variable (u), then just do power rule on that and multiply by the derivative of the substitution variable to account for the substitution.

This is quite fundamental. If you've been answering mechanically to this point, I warn you that just copying what I've written will get you sussed, but I feel the need to illustrate here. Someone tell me if this isn't allowed.

https://imgur.com/a/9CWPxRQ

(edited 1 year ago)
Original post by gdunne42
Have you been taught how to use the chain rule? The steps you are attempting to follow do work if applied correctly but without a real understanding of the reasons why.

Following the suggested method here and a different example

if 𝑖 = (4𝑡 + 5)^10

if you first multiply the bracket by the original power you get 10(4𝑡 + 5)^10
if you then also multiply by the differentiated content of the bracket and reduce the power by 1 your result should be
(10)(4)(4𝑡 + 5)^9
d𝑖/dt = 40(4𝑡 + 5)^9

Ah that makes it abit more understandable applying this way then factoring in my t=3 to my equation has given me 32928 which seems more suitable think ill have to practise this abit more to fully get my head around the chain rule the work book has roughly gone over it but im still struggling getting my head around it