Differentiate g(t)=t^8cos(t)

Question

I got .......t^8(-sint)+cost(8t^7)

then.......8t^7cost-t^8sint

lastly gcf t^7(8cost+tsint) why isnt that right????

Answer 1

g(t) = t⁸cos(t)

Use the product rule: (xy)' = x'y + xy' = xy' + x'y

g '(t) = 8t⁷cos(t) -t⁸sin(t) = t⁷(8cos(t) -tsin(t))

I think your error is your last answer has + instead of -

Answer 2

Your first statement shows the correct answer:

g'(t) = -t⁸sin(t) + 8t⁷cos(t)

At this point you could factor a GCF of t⁷:

t⁷(8cos(t) - tsin(t)) => this is different than your final answer that contains a + instead of "-".