What is d/dx [sin(5x^2)]?

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Multiple Choice

What is d/dx [sin(5x^2)]?

Explanation:
Use the chain rule: for sin(u) the derivative is cos(u) times the derivative of u. Here the inner function is u = 5x^2, whose derivative is 10x. Put it together: d/dx [sin(5x^2)] = cos(5x^2) · 10x = 10x cos(5x^2). This is the correct result because it correctly applies the outer derivative (cos) and the inner derivative (10x).

Use the chain rule: for sin(u) the derivative is cos(u) times the derivative of u. Here the inner function is u = 5x^2, whose derivative is 10x. Put it together: d/dx [sin(5x^2)] = cos(5x^2) · 10x = 10x cos(5x^2). This is the correct result because it correctly applies the outer derivative (cos) and the inner derivative (10x).

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