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Product and chain rule

  • Thread starter Rasine
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  • #1
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i am having trouble with this one problem. maybe you can tell me where i am going wrong.

find h'(t) if h(t)=(t^6-1)^5(t^5+1)^6

so i am using product rule and to find the derivatives of each expression i am using chain rule...

so i get h'(t)=30t^4(t^6-1)^4(t^5+1)^6+30^4(t^5+1)^5(t^6-1)^5


is that right..or what is wrong with it?
 

Answers and Replies

  • #2
D H
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Not quite right. The factors [itex](t^6-1)^4(t^5+1)^6[/itex] and [itex](t^5+1)^5(t^6-1)^5[/itex] in the two terms are correct, but the factors involving a power of [itex]t[/itex] are not.

What is [itex]\frac d{dt}\left((t^6-1)^5\right)[/itex] ?
 
  • #3
HallsofIvy
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i am having trouble with this one problem. maybe you can tell me where i am going wrong.

find h'(t) if h(t)=(t^6-1)^5(t^5+1)^6

so i am using product rule and to find the derivatives of each expression i am using chain rule...

so i get h'(t)=30t^4(t^6-1)^4(t^5+1)^6+30^4(t^5+1)^5(t^6-1)^5

is that right..or what is wrong with it?
The derivative of (t6-1)5 is 5(t6-1)4(6t5= 30t5(t6-1)4. I think you've missed a power of t in the first term above.

The derivative of (t5+ 1)6 is 6(t5+ 1)5(5t4)= 30t4(t5+ 1)5
You seem to be missing a "t"! (30^4 instead of 30t^4!)
 

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