Question

If `y=(x^3)ln(x^3)` then `dy/dx=`?

Answer 1

`y=(x^3)ln(x^3)`

Applying product rule,

`dy/dx=(x^3)'ln(x^3) + (x^3)[ln(x^3)]'`

`dy/dx = 3x^2ln(x^3) +cancel x^3*(1/cancelx^3*3x^2)`

`dy/dx = 3x^2ln(x^3) + 3x^2`

`dy/dx = 3x^2(ln(x^3) + 1)`

Answer 2

Use `ln(x^3) = 3lnx` to write:

`y = 3x^3lnx`

Now use the product rule to differentiate.

`y' = 9x^2lnx + 3x^3 * 1/x` And simplify

`y' 9x^2lnx+3x^2 = 3x^2(1+3lnx)`