11.09 Product Rule

Differentiate the function $g\left(t\right)=\left(2t^3-3\right)\left(3-t\right)$g(t)=(2t3−3)(3−t). You may use the substitutions $u=2t^3-3$u=2t3−3 and $v=3-t$v=3−t.

Differentiate the function $g\left(y\right)=\left(7y^4-y^2\right)\left(y^2-5\right)$g(y)=(7y4−y2)(y2−5). You may use the substitutions $u=7y^4-y^2$u=7y4−y2 and $v=y^2-5$v=y2−5.

We want to differentiate $y=x^6\left(x^4+4\right)$y=x6(x4+4) using the product rule.

Let $u=x^6$u=x6 and $v=x^4+4$v=x4+4.