Differentiate with respect to x y=(x^3)ln2x

To be able to differentiate this we need to use the product rule as we want to differentiate two functions multiplied together. The product rule states that if y=uv, then : dy/dx= u dv/dx + v du/dx. Let u= x^3 and v= ln2x. Then du/dx= 3x^2 and dv/dx= 2/2x. Putting this together using the formula gives: dy/dx= x^3 * 2/2x + ln2x * 3x^2. This simplifies to dy/dx= 3x^2ln2x+x^2