find the derivitive of h(t)=(t^7 - 1)^6 (t^6 + 1)^7?

Question

pls help... and if u can, can you also explain . thank you

Answer 1

This is just an application of the product rule and the chain rule. You have the product of (t^7 - 1)^6 and (t^6 + 1)^7 so the first thing you have to do is differentiate each of these. Using the chain rule the first differentiates to 6*(t^7 - 1)^5*7t^6
= 42t^6(t^7 - 1)^5. I'll leave you to do the other. Then put them together with the product rule.

Answer 2

y=u*p ==> y'=u'p+p'u
y=(u)^n ==> y'=n(u)^(n-1)*u'
(u & p are functions)
f(x)=(t^7-1)^6 ==> f'(x)=6(t^7-1)^5 *7t^6
g(x)=(t^6 + 1)^7 ===>g'(x)=7(t^6 + 1)^6* 6t^5
y=f(x)g(x)
y'=f'(x)g(x)+g'(x)f(x)
y'=6(t^7-1)^5 *7t^6*(t^6 + 1)^7+7(t^6 + 1)^6* 6t^5 *(t^7 - 1)^6