All Derivative Rules + Implicit

What is dy/dx? 

 $y^3=6x$  

•  $\frac{2}{y^2}$  

•  $\frac{3}{y^3}$  

•  $3y^2$  

•  $\frac{2x}{y^2}$  

What is dy/dx?

 $xy=1$  

•  $\frac{x}{y}$  

•  $-\frac{x}{y}$  

•  $\frac{y}{x}$  

•  $-\frac{y}{x}$  

What is dy/dx?

 $x^2+y^2=1$  

•  $-\frac{y}{x}$  

•  $\frac{x}{y}$  

•  $-\frac{x}{y}$  

•  $\frac{y}{x}$  

What is dy/dx?

 $y=\arctan\left(x^2\right)$  

•  $\frac{1}{1+x^4}$  

•  $\frac{2x}{1+x^4}$  

•  $\frac{4x^3}{1+x^4}$  

•  $\frac{1}{1+x^2}$  

Tags

CCSS.HSF.TF.B.7

What is dy/dx?

 $y=3^{\sqrt{x}}$  

•  $\frac{3^{\sqrt{x}}\cdot\ln\left(3\right)}{\sqrt{x}}$  

•  $3^{\sqrt{x}}\cdot\ln\left(3\right)\cdot\sqrt{x}$  

•  $3^{\sqrt{x}}\cdot\ln\left(3\right)$  

•  $\frac{3^{\sqrt{x}}\cdot\ln\left(3\right)}{2\sqrt{x}}$  

What is dy/dx?

 $y=2\ln\left(3-x\right)$  

•  $\frac{2}{3-x}$  

•  $\frac{-2}{3-x}$  

•  $\frac{1}{3-x}$  

•  $3-x$  

What is dy/dx?

 $y=x\cdot\arcsin\left(x\right)$  

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

•  $\frac{x+1}{\sqrt{1-x^2}}$  

•  $\frac{x}{\sqrt{1-x^2}}$  

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

At what point does the curve given by

 $x=t^2-2t$   and  $y=t+1$  
have a vertical tangent?

• (1, 0)

• (3, 0)

• (-1,2)

• (1, 2)

What is dy/dx?
 $y=\cot^3\left(\sqrt{x^2-1}\right)$  

•  $-3\cot^2\left(\sqrt{x^2-1}\right)\csc^2\left(\sqrt{x^2-1}\right)$  

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

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

•  $-\frac{3\csc^4\left(\sqrt{x^2-1}\right)}{2\sqrt{x^2-1}}$  

At what points does the curve
 $x^2+y^2=1$  

have tangents with a slope of 1?

hint: you don't need calculus for this! 

•  $\left(-\frac{\sqrt{2}}{2},\ \frac{\sqrt{2}}{2}\right)\ and\ \left(-\frac{\sqrt{2}}{2},\ -\frac{\sqrt{2}}{2}\right)$  

•  $\left(\frac{\sqrt{2}}{2},\ \frac{\sqrt{2}}{2}\right)\ and\ \left(-\frac{\sqrt{2}}{2},\ -\frac{\sqrt{2}}{2}\right)$  

•  $\left(-\frac{\sqrt{2}}{2},\ \frac{\sqrt{2}}{2}\right)\ and\ \left(\frac{\sqrt{2}}{2},\ -\frac{\sqrt{2}}{2}\right)$  

•  $\left(-\frac{\sqrt{2}}{2},\ \frac{\sqrt{2}}{2}\right)\ and\ \left(-\frac{\sqrt{2}}{2},\ -\frac{\sqrt{2}}{2}\right)$