How do you differentiate $g (t) = (\frac{2}{t} + t^{5}) (t^{3} + 1)$ $g(t)=(2/t+t^5)(t^3+1)$ using the product rule?

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Answer 1 · 2017-01-21T22:44:38

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

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

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

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