Question

I am 99% sure this is correct but...

Answer 1

y= exp(x) sin(x)
y' = exp(x) cos(x) + exp(x) sin(x) = exp(x) (sin(x) + cos(x))

(y')^2 = exp(2x) ( sin x + cos x)^2
= exp(2x) (sin^2 x + cos^2 x + 2 sin x cos x)
now use trig identities: sin^2 x + cos^2 x = 1 and sin 2x = 2 sin x cos x
to get
\[ (y')^2 = e^{2x}(1+\sin 2x)\]
use that result in
\[ \sqrt{1 + (y')^2} \]

Answer 2

So is what I marked correct?

Answer 3

yes