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Show as many steps as possible with proper formatting, thanks!

Use logarithmic differentiation to find the derivative of the function. Y=x3 sin x

Solution

y = x^(3 sin x)

ln y = ln x^(3 sin x)

ln y = 3 sin x ln x

d/dx (ln y) = d/dx (3 sin x ln x)

y\'/y = 3(cos x ln x + (sin x)/x)

y\'/y = 3(1/x)(x cos x ln x + sin x)

y\' = 3y(1/x)(x cos x ln x + sin x)

y\' = 3x^(3 sin x)(1/x)(x cos x ln x + sin x)

y\' = 3x^(3 sin x - 1)(x cos x ln x + sin x)

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