Chain Rule

 $1-\frac{8}{t^2}$  

 $1-\frac{8}{t}$  

 $t-\frac{8}{t^2}$  

 $1+\frac{8}{t^2}$  

 $-\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$  

 $\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$  

 $-\frac{1}{\left(q+9\right)^{\frac{3}{2}}}$  

 $-\frac{1}{\sqrt{q+9}}$  

 $\frac{2x^3-3x^2}{\left(x-1\right)^2}$  

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

 $\frac{-2x^3-3x^2}{\left(x-1\right)^2}$  

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

 $\frac{3e^t}{\left(2e^t+1\right)^3}$  

 $\frac{3e^t}{\left(2e^t+1\right)^2}$  

 $\frac{3e^t}{\left(2e^t+1\right)^{ }}$  

 $\frac{e^t}{\left(2e^t+1\right)^2}$  

 $\frac{2x^{\frac{1}{3}}}{3}+ex^e$  

 $\frac{2}{3x^{\frac{1}{3}}}+ex^{\left(e-1\right)}$  

 $\frac{2x^{\frac{1}{3}}}{3}+ex^{\left(e-1\right)}$  

 $\frac{2}{3x^{\frac{1}{3}}}+ex^e$  

 $\left(12x+4\right)\left(2x^2+4\right)^2$  

 $3\left(2x^2+4\right)^2$  

 $12x\left(2x^2+4\right)^2$  

 $12\left(2x^2+4\right)^2$  

 $\frac{-3\sec\theta}{\left(\sec\theta+\tan\theta\right)^3}$  

 $-3\left(\sec\theta+\tan\theta\right)^{-4}\left(\tan^2\theta+\sec\theta\tan\theta\right)$  

 $-3\left(\sec\theta+\tan\theta\right)^{-4}$  

 $-3\left(\sec\theta+\tan\theta+\sec^2\theta\right)^{-4}$  

 $2e^x\sin x$  

 $2e^x\left(\sin x-\cos x\right)+2e^x$  

 $0$  

 $4e^x\left(\sin x-\cos x\right)$  

 $\frac{-5}{\sqrt{10t+12}}\sin\sqrt{10t+12}$  

 $\frac{-1}{2\sqrt{10t+12}}\sin\sqrt{10t+12}$  

 $-\sin\sqrt{10t+12}$  

 $-\sin\left(\frac{5}{\sqrt{10t+12}}\right)$  

 $-\frac{1}{x}$  

 $\frac{1}{2x}$  

 $\frac{1}{x}$  

 $\frac{-1}{2x}$