Solution: dy/dx = -10xsin(5x^2) by the chain rule.
Steps: 8
Step 1: Identify the function y = cos(5x^2).
Step 2: Recognize that we need to find the derivative dy/dx using the chain rule.
Step 3: The chain rule states that if you have a function inside another function, you take the derivative of the outer function and multiply it by the derivative of the inner function.
Step 4: The outer function is cos(u), where u = 5x^2. The derivative of cos(u) is -sin(u).
Step 5: Now, find the derivative of the inner function u = 5x^2. The derivative of 5x^2 is 10x.
Step 6: Apply the chain rule: dy/dx = -sin(5x^2) * (derivative of 5x^2).
Step 7: Substitute the derivative of the inner function: dy/dx = -sin(5x^2) * 10x.
Step 8: Combine the terms: dy/dx = -10x * sin(5x^2).
