Chapter 3 - Section 3.2 - The Product and Quotient Rules - 3.2 Exercises - Page 188: 16

$y'=-\dfrac{3t^{2}+4t}{(t^{3}+2t^{2}-1)^{2}}$

$y=\dfrac{1}{t^{3}+2t^{2}-1}$ Differentiate using the quotient rule: $y'=\dfrac{(t^{3}+2t^{2}-1)(1)'-(1)(t^{3}+2t^{2}-1)'}{(t^{3}+2t^{2}-1)^{2}}=...$ $...=\dfrac{(t^{3}+2t^{2}-1)(0)-(1)(3t^{2}+4t)}{(t^{3}+2t^{2}-1)^{2}}=...$ Evaluate the products and simplify: $...=\dfrac{-3t^{2}-4t}{(t^{3}+2t^{2}-1)^{2}}=-\dfrac{3t^{2}+4t}{(t^{3}+2t^{2}-1)^{2}}$