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How do you differentiate #g(t)=(2/t+t^5)(t^3+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#

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