Steve S. answered • 04/06/14
Tutor
5
(3)
Tutoring in Precalculus, Trig, and Differential Calculus
g(p) = (10^p)(e^(2p))
= ((e^ln(10))^p)(e^(2p))
= (e^(p ln(10)))(e^(2p))
g'(p) = (e^(p ln(10)))'(e^(2p))+(e^(p ln(10)))(e^(2p))'
= (e^(p ln(10)))(ln(10))(e^(2p))+(e^(p ln(10)))(e^(2p))(2)
= (10^p)(ln(10))(e^(2p))+(10^p)(e^(2p))(2)
= (ln(10)+2)(10^p)(e^(2p))
= (ln(10)+2)(g(p))
= ((e^ln(10))^p)(e^(2p))
= (e^(p ln(10)))(e^(2p))
g'(p) = (e^(p ln(10)))'(e^(2p))+(e^(p ln(10)))(e^(2p))'
= (e^(p ln(10)))(ln(10))(e^(2p))+(e^(p ln(10)))(e^(2p))(2)
= (10^p)(ln(10))(e^(2p))+(10^p)(e^(2p))(2)
= (ln(10)+2)(10^p)(e^(2p))
= (ln(10)+2)(g(p))
