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 2xcos(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