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Differentiate the function: y = sin(x^2)*ln(5x)

We are tasked with differentiating y = sin(x2)*ln(5x)

This function is actually a product of the functions:

sin(x2) and ln(5x)

Therefore the product rule will be required.

First let's calculate the derivatives of our individual functions before combining them.

The derivative of sin(x2) is 2x*cos(x2) using the chain rule.

The derivative of ln(5x) is 1/x.

Now to combine these using the product rule. Our answer will be:

2x*cos(x2)*ln(5x) + sin(x2)*1/x

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