I have y = sin^2(3^(x))

Question

which I rewrite as
y = (sin(3^(x)))^2

I got the derivative using the chain rule as the following

y' = 3(sin(3^x))^2 (cos(3x)) (3^(x)(ln(3))

Can anyone confirm whether this is right/wrong? Thanks

Answer 1

well, if y = sin^2(u)
y' = 2 sinu cosu u'
u' = ln3 3^x

y' = 2ln3 3^x sin(3^x) cos(3^x)
= ln3 3^x sin(2*3^x)

I think you got some of your 3's mixed up as powers of sin.

You appear to have taken the derivative of

sin^3 (3^x)