Calculus 10th Edition

Rewrite: $4x^3$; Differentiate: $(4)(3)(x^{3-1})$; Simplify: $12x^2$.
To simplify, just use the same index rule to take $x^{-3}$ to the numerator; hence, the function becomes $4x^3$. To differentiate just use the power rule to find the derivative of $x^3$ which is $3x^{3-1}$ so the overall derivative is $(4)(3)(x^{3-1})$. To simplify, just multiply the constants together to get $12x^2$.