If y = x sin x, then dy/dx =
To find the derivative of y with respect to x, we can use the product rule and the chain rule
To find the derivative of y with respect to x, we can use the product rule and the chain rule. Let’s differentiate each term step by step:
1. The derivative of x is 1.
2. The derivative of sin x is cos x.
3. To differentiate the product of two functions, we use the product rule, which states that the derivative of the product f(x)g(x) is f'(x)g(x) + f(x)g'(x).
Applying these rules, we can find the derivative of y = x sin x:
dy/dx = (x)(cos x) + (1)(sin x)
= x cos x + sin x
Therefore, the derivative of y = x sin x is dy/dx = x cos x + sin x.
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