To find the derivative of f(x) = x sin x using the product rule, we differentiate each function and apply the product rule.
Let u = x and v = sin x.
Using the product rule, the derivative of f(x) is given by:
f'(x) = u'v + uv'
Differentiating u = x, we have:
u' = 1
Differentiating v = sin x, we have:
v' = cos x
Substituting these values into the product rule formula, we get:
f'(x) = (1)(sin x) + (x)(cos x)
f'(x) = sin x + x cos x
Therefore, the derivative of f(x) = x sin x is f'(x) = sin x + x cos x.
Find the derivative of each of the following functions using the product rule
a. f(x) =x sin x
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