Exit Slip 2.2 Derivatives - Power Rule & Rates of Change

Find the derivative of the given equation

f(x) = x³ + x² + 3

• 3x² + 2x

• 3x + 2x

• 3x² + 2x + 3

• x³ + x²

Find the slope of f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

Differentiate y= 12x^-2

• 24x^-1
• -24x^-3
• -24x^-1
• 6x^-3

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

The derivative of 

• y'=2x-x^-2
• y'=x^-1+8x
• y'=x^-2+8x
• y=8x-x^-2

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.1

At which x-value is f continuous but not differentiable?

• a
• b
• c
• d

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the derivative of:  $f\left(x\right)\ =\ \sqrt{x}$  

•  $\frac{1}{2}x^2$  

•  $\frac{1}{2\sqrt{x}}$  

•  $\frac{1}{\sqrt{x}}$  

•  $\frac{1}{2x^2}$  

Tags

CCSS.HSF.IF.C.8

CCSS.HSN.RN.A.1

CCSS.HSN.RN.A.2

Find the derivative of  $f\left(x\right)\ =\ \frac{1}{x^5}$  

•  $5x^4$  

•  $-5x^6$  

•  $-\frac{5}{x^6}$  

•  $\frac{1}{5x^6}$  

Find the derivative of  $f\left(x\right)\ =\ \frac{1}{2\sqrt{x}}$  

•  $-\frac{1}{4\sqrt{x^3}}$  

•  $-\frac{1}{\sqrt{x^3}}$  

•  $-x^2$  

•  $-4x^2$  

Find the derivative of  $f\left(x\right)\ =\ \left(3\ -\ \sqrt{x}\right)\left(3\ -\ \sqrt{x}\right)$  

•  $9-6\sqrt{x}-x$  

•  $-\frac{3}{\sqrt{x}}+1$  

•  $1-\frac{1}{3\sqrt{x}}$  

•  $-\frac{1}{\sqrt{3x}}+1$  

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

Calculate the derivative of  $f\left(x\right).$  

•  $4x^2+9$  

•  $8x$  

•  $8x+12$  

•  $4x^2+12x+9$