Questions: 2.9 The Quotient Rule Calculus Name: 1. h(x) = (r^2 + tr - 1) / (x - 1) h'(x) = L(2x + 4)(x - 3)^-3 - (x^2(4x - 1) + 1) 2(x^2) f'(x) = (2x^2 - 6x + 4x - 12 - x^2 - 4x + 1) / (x - 3)^2 (x^2 - 6x - 11) / (x - 3)^2 2. g(x) = set / (2 sin x) 3. f(x) = enas / (z - 16) 4. g(x) = (4x^3 - 5x^2 + 5x) / x^2 5. h(x) = 5x^2 / ln x (4x^3 - 5x^2 + 5x) = 12x^2 - 10x + 5 g'(x) = (12x^2 - 10x + 5)(x^2) - (4x^3 - 5x^2 + 5x)(2x) / (x^2)^2 g'(x) = (4x^4 - 5x^2) / x^4 g'(x) = 4 - 5/x^2 6. f(x) = (x + 2) / (x^2 + 2) 7. h(x) = (8x^3 + 4x^2 - 9x) / 2x

Transcript text: 2.9 The Quotient Rule Calcalus Name: 1. $h(x)=\frac{r^{2}+t r-1}{x-1}$ \[ \begin{array}{l} h^{\prime}(x)=L(2 x+4)(x-3)^{-3}-\left(x^{2}(4 x-1)+1\right) 2\left(x^{2}\right. \\ f^{\prime}(x)=\left(2 x^{2}-6 x+4 x-12-x^{2}-4 x+1\right) /\left(x-3^{2}=\right. \\ \frac{\left(x^{2}-6 x-11\right.}{(x-3)^{2}} \end{array} \] 2. $g(x)=\frac{\operatorname{set}}{2 \sin x}$ 3. $f(x)=\frac{e n a s}{z-16}$ 4. $g(x)=\frac{4 x^{3}-5 x^{2}+5 x}{x^{2}}$ 5. $h(x)=\frac{5 x^{2}}{\ln x}$ \[ \begin{array}{l} \left(4 x^{3}-5 x^{2}+5 x\right)=12 x^{2}-10 x+5 \\ g^{\prime}(x)=\frac{\left.12 x^{2}-10 x+5\right)\left(x^{2}\right)-\left(4 x^{3}-5 x^{2}+5 x\right)(2 x)}{\left(x^{2}\right)^{2}} \\ g^{\prime}(x)=\frac{4 x^{4}-5 x^{2}}{x^{4}} \\ g^{\prime}(x)=4-\frac{5}{x^{2}} \end{array} \] 6. $f(x)=\frac{x+2}{x^{2}+2}$ 7. $h(x)=\frac{8 x^{3}+4 x^{2}-9 x}{2 x}$