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).
Chain Rule – The chain rule is a fundamental differentiation technique used to differentiate composite functions.
Trigonometric Functions – Understanding the derivatives of trigonometric functions, such as cosine, is essential for solving problems involving them.
Polynomial Functions – Recognizing and differentiating polynomial expressions, such as 5x^2, is crucial in calculus.
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