Final answer:
To differentiate y = √(3^(sin(2x))), use the chain rule. Substitute u = 3^(sin(2x)). Differentiate u and y with respect to x. Apply the chain rule and simplify to find the derivative dy/dx.
Step-by-step explanation:
To differentiate y = √(3^(sin(2x))), we can use the chain rule.
Let u = 3^(sin(2x)), so y = √u.
Now, we can differentiate u and y with respect to x.
The derivative of u with respect to x is :
du/dx = (ln(3) *cos(2x)) * (3^(sin(2x))).
The derivative of y with respect to x is:
dy/dx = (1/2) * (u^(-1/2)) * du/dx.
Combining these results, we find that:
dy/dx = (1/2) * (3^(sin(2x))^(-1/2)) * (ln(3) *cos(2x)) * (3^(sin(2x))).