Chain Rule

Find  $\frac{dv}{dt}\ if\ v=t+\frac{8}{t}$  

•  $1-\frac{8}{t^2}$  

•  $1-\frac{8}{t}$  

•  $t-\frac{8}{t^2}$  

•  $1+\frac{8}{t^2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Find  $\frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}}$  

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

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

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

•  $-\frac{1}{\sqrt{q+9}}$  

Tags

CCSS.HSN.RN.A.2

Find  $\frac{dy}{dx}\ if\ y=\frac{x^3}{x-1}$  

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

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

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

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

Tags

CCSS.HSA.APR.D.6

 $\frac{ds}{dt}\ if\ s=\frac{3e^t}{2e^t+1}$  Find

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

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

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

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

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

 $\frac{dy}{dx}\ if\ y=^3\sqrt{x^2\ }+x^e$  Find

•  $\frac{2x^{\frac{1}{3}}}{3}+ex^e$  

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

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

•  $\frac{2}{3x^{\frac{1}{3}}}+ex^e$  

Tags

CCSS.HSN.RN.A.2

 $\frac{dy}{dx}\ if\ y=\left(2x^2+4\right)^3$  Find

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

•  $3\left(2x^2+4\right)^2$  

•  $12x\left(2x^2+4\right)^2$  

•  $12\left(2x^2+4\right)^2$  

Tags

CCSS.HSA.APR.A.1

 $\frac{dr}{dt}\ if\ r=\left(\sec\theta+\tan\theta\right)^{-3}$  Find

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

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

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

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

Tags

CCSS.HSA.SSE.B.3

 $\frac{dy}{dx}\ if\ y=e^x\left(\sin x-\cos x\right)$  Find

•  $2e^x\sin x$  

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

•  $0$  

•  $4e^x\left(\sin x-\cos x\right)$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

 $\frac{dy}{dt}\ if\ y=\cos\sqrt{10t+12}$  Find

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

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

•  $-\sin\sqrt{10t+12}$  

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

 $\frac{dy}{dx}if\ y=\ln2x$  Find

•  $-\frac{1}{x}$  

•  $\frac{1}{2x}$  

•  $\frac{1}{x}$  

•  $\frac{-1}{2x}$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2