Question

differentiate y=x^4lnx-(1/2)x^2

Answer 1

Use the chain rule to get \[y'=4x^3\ln x + x^4\tfrac{1}{x}-x\] which simplifies to \[y'=4x^3\ln x+x^3 - x\]

Answer 2

y=x^4lnx-(1/2)x^2
y'=x^4/x+4x^3lnx-(1/2)2x
y'=x^3+4x^3lnx-x