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

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

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

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

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

(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

(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

(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

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

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

^See linked image for explanation

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

^See linked image for explanation

(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

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

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