If \(y = x \sin x\), Find \(\dfrac{d^2y}{d^2x}\)
Question 1 Report
If \(y = x \sin x\), Find \(\dfrac{d^2y}{d^2x}\)
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.
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