How do you differentiate g(t)=(2/t+t^5)(t^3+1)g(t)=(2t+t5)(t3+1) using the product rule?

1 Answer
Jan 21, 2017

g'(t) = (-2t^-2 +5t^4)(t^3+1) + (2t^-1 +t^5)*3t^2

Explanation:

The product rule says if:
f(x) = u(x)*v(x)
then
f'(x) = u'(x)*v(x) + u(x)*v'(x)

In your equation g(t)
Let
u(t) = 2t^-1 + t^5 then u'(t) = -2t^-2 + 5t^4
and
v(t) = t^3+1 then v'(t) = 3t^2

So
g'(t) = u'(x)*v(x) + u(x)*v'(x)

g'(t) = (-2t^-2 +5t^4)(t^3+1) + (2t^-1 +t^5)*3t^2