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

Question

3204 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-09T18:01:10

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

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

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

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

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

Answer 2 · 2018-04-09T18:02:57

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

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

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