use log differentiation to find the derivative

Question

y=(sqrt(x) e^(x^2-x) (x^2 + 1)^(3/2))/(x^2 -4)

Answer 1

Step 1:

The function is .

Apply logarithm on each side.

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Quotient rule of logarithms: .

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Product rule of logarithms: .

Power rule of logarithms: .

Substitute value of above expression in .

Step 2:

Differentiate with respect to on each side.

Use the logarithmic differentiation: .

Substitute in above expression.

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Solution: 

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