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
TC
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