To find the derivative d/dx (y) when x = 3 for the function y = sin(f(x^2)), we need to apply the chain rule. After taking the derivative with respect to x, we evaluate it at x = 3.
The final answer is cos(f(9)) * f'(9) * 6, where f'(x^2) is the derivative of f(x^2) with respect to x.
To find ∂/∂x (y) when x = 3, we need to take the derivative of the function y = sin(f(x^2)) with respect to x and then evaluate it at x = 3.
Let's start by applying the chain rule. Let u = f(x^2), so y = sin(u).
Using the chain rule, we have:
∂y/∂x = ∂y/∂u ∂u/∂x
= cos(u) ∂f/∂x^2 2x, using the chain rule for u = f(x^2)
= cos(f(x^2)) f'(x^2) 2x, where f'(x^2) is the derivative of f(x^2) with respect to x.
Now, evaluate the derivative at x = 3:
∂y/∂x = cos(f(3^2)) f'(3^2) * 2(3)
= cos(f(9)) f'(9) 6
Since we don't have any information about the specific function f(x), we cannot simplify further without knowing the function.
So the final answer is ∂y/∂x = cos(f(9)) f'(9) 6.