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What is the derivative of y = x^1/2?
How do you use the chain rule for a function like y = sin(x^2)?
To use the chain rule for y = sin(x^2), we recognize that the function inside the sine function is x^2, and the sine function is the outer function. Therefore, let u = x^2 and v = sin(u). Then, using the chain rule, we have dy/dx = (cos(u)) * (d/dx)(u) = 2x * cos(x^2). Substituting back in, we have dy/dx = 2x cos(x^2).