Question

Find y' and y''.

y = x^2 ln(9x)

y' =
y''=

Answer 1

Product rule, Power rule, Chain rule. Those are the rules you need to use. @TachiHere

Answer 2

I'll do the first one for you:\[\bf y'=[x^2\ln(9x)]'=(x^2)'\ln(9x)+x^2(\ln(9x))'=2xln(9x)+x^2\left( \frac{ 1 }{ \cancel9x } \right)\cancel9\]\[\ \ \ \bf = 2xln(9x)+x\]Also note that the derivative of ln(u) where 'u' is a function of 'x' is:\[\bf \ln(u)=\frac{ 1 }{ u }*\frac{ du }{ dx }\]Now can you find y''? @TachiHere

Answer 3

2x ln(9x) is the product of 2 functions so use product rule for tis part