If y = 𝑠𝑖𝑛𝑥𝑥2, dy/dx =

To find the derivative of y = sin(x^2), we will use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 1: Identify the outer and inner functions. Here, the outer function is sin(u) and the inner function is u = x^2.

Step 2: Find the derivative of the outer function. The derivative of sin(u) with respect to u is cos(u).

Step 3: Find the derivative of the inner function. The derivative of x^2 with respect to x is 2x.

Step 4: Apply the chain rule. According to the chain rule, dy/dx = (dy/du) * (du/dx). Substituting the derivatives we found in steps 2 and 3, we get dy/dx = cos(u) * 2x.

Step 5: Substitute u = x^2 back into the equation to get the final answer. So, dy/dx = 2x * cos(x^2).