Answer:
y" = sec(x) · [sec²(x) + tan²(x)]
Step-by-step explanation:
Remember your Trig derivatives.
Derivative of sec(x) is sec(x)tan(x)
Derivative of tan(x) = sec²(x)
Product Rule:
f'(x)g(x) + f(x)g'(x)
Step 1: Find 1st derivative of sec(x) (Trig Rule)
y' = sec(x)tan(x)
Step 2: Find 2nd derivative (Product Rule and Trig Rule)
y" = sec(x)sec²(x) + sec(x)tan(x)tan(x)
y" = sec³(x) + sec(x)tan²(x)
y" = sec(x) · [sec²(x) + tan²(x)]
