If y = x sin x, Find d2yd2x

If y = x sin x, Find $\frac{d^{2}y}{d^{2}x}$

Answer Details

To find the second derivative of y = x sin x, we need to differentiate the function twice with respect to x. First, let's find the first derivative: y' = (x cos x) + (sin x) Using the product rule and the derivative of sin x. Next, we can find the second derivative: y'' = [(x cos x) + (sin x)]' = (cos x - x sin x) + cos x Using the product rule and the derivative of cos x. Therefore, the second derivative of y = x sin x is y'' = 2 cos x - x sin x.