Troubleshooting Product and Chain Rule for h(t) Derivatives

[Rasine]

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?

 

[D H]

Not quite right. The factors $(t^6-1)^4(t^5+1)^6$ and $(t^5+1)^5(t^6-1)^5$ in the two terms are correct, but the factors involving a power of $t$ are not.

What is $\frac d{dt}\left((t^6-1)^5\right)$ ?

 

[HallsofIvy]

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)<sup>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!)</sup>