Answer to Question #331688 in Calculus for Olga

Question

Find the second derivative of the following function:

F(x)=3x^3 − 1 / x + e^2x.

is

a.18x − ln x + 4e^2x

b.18x − 2 / x^3 + 2e^2x

c.18x + 2 / x^3 + 4e^2x

d.18x − 2 / x^3+ 4e^2x

Answer 1

$y' = {\left( {3{x^3} - \frac{1}{x} + {e^{2x}}} \right)^\prime } = 9{x^2} + \frac{1}{{{x^2}}} + 2{e^{2x}}$

$y'' = {\left( {9{x^2} + \frac{1}{{{x^2}}} + 2{e^{2x}}} \right)^\prime } = 18x - \frac{2}{{{x^3}}} + 4{e^{2x}}$

Answer: d