Chain Rule ALL

 $y=\frac{\left(-x^2+5\right)^{-5}}{x^5+2}$  

•  $\frac{dy}{dx}=\frac{5x\left(3x^5+4-5x^3\right)}{\left(x^5+2\right)\left(-x^2+5\right)^6}$  

•  $\frac{dy}{dx}=5x\left(-x^2+5\right)^4\left(3x^5+4-5x^3\right)$  

•  $\frac{dy}{dx}=\frac{5x\left(3x^5+4-5x^3\right)}{\left(x^5+2\right)^2\left(-x^2+5\right)^6}$  

•  $\frac{dy}{dx}=\frac{5x\left(3x^5+4-5x^3\right)}{\left(-x^2+5\right)^6}$  

 $y=\left(-2x^4+1\right)^{\frac{1}{3}}\left(5x+3\right)$  

•  $\frac{dy}{dx}=\frac{-70x^4+15-24x^3}{3\left(-2x^4+1\right)^{\frac{2}{3}}}$  

•  $\frac{dy}{dx}=5\left(-2x^4+1\right)^{\frac{1}{3}}$  

•  $\frac{dy}{dx}=-\frac{80x^3}{3\left(-2x^4+1\right)^{\frac{2}{3}}}$  

•  $\frac{dy}{dx}=\frac{15\left(-2x^4+1\right)^{\frac{2}{3}}-8x^3}{3\left(-2x^4+1\right)^{\frac{2}{3}}}$  

 $y=\left(\frac{x^5+3}{-x^2-3}\right)^{\frac{1}{4}}$  

•  $\frac{dy}{dx}=\frac{3x\left(-x^5-5x^3+2\right)}{\left(-x^2-3\right)^2}$  

•  $\frac{dy}{dx}=\frac{3x\left(-x^5-5x^3+2\right)}{4\left(x^5+3\right)^{\frac{3}{4}}\left(-x^2-3\right)^{\frac{5}{4}}}$  

•  $\frac{dy}{dx}=\frac{3x\left(-x^5-5x^3+2\right)}{\left(x^5+3\right)^{\frac{3}{4}}\left(-x^2-3\right)^{\frac{5}{4}}}$  

•  $\frac{dy}{dx}=\frac{\left(-x^2-3\right)^{\frac{3}{4}}}{4\left(x^5+3\right)^{\frac{3}{4}}}$  

 $y=\left(3x^2+2\right)^2\left(x^3-3\right)$  

•  $\frac{dy}{dx}=3x\left(12x^2+8+x\right)$  

•  $\frac{dy}{dx}=72x^3\left(3x^2+2\right)$  

•  $\frac{dy}{dx}=\left(3x^2+2\right)^2\left(3x^2\right)$  

•  $\frac{dy}{dx}=3x\left(3x^2+2\right)\left(7x^3+2x-12\right)$