Calculus Chapter 2 Test

 $f\left(x\right)=6x+7$ 

Discuss the process and steps to find the derivative of this functions using the limit process. Also give the final answer.

Tags

CCSS.8.EE.B.5

 $f\left(x\right)=23x$  

What rules are used to find the derivative of the following expression:

(select all that apply)

• Constant rule

• Power rule

• Product rule

• Quotient rule

• Chain rule

 $f\left(x\right)=4x^2+15$  

What rules are used to find the derivative of the following expression:

(select all that apply)

• Constant rule

• Power rule

• Product rule

• Quotient rule

• Chain rule

 $f\left(x\right)=18-4$  

What rules are used to find the derivative of the following expression:

(select all that apply)

• Constant rule

• Power rule

• Product rule

• Quotient rule

• Chain rule

 $f\left(x\right)=6x^3\sin x$  

What rules are used to find the derivative of the following expression:

(select all that apply)

• Constant rule

• Power rule

• Product rule

• Quotient rule

• Trig rule

 $f\left(x\right)=\frac{3x^2}{3x+4}$  

What rules are used to find the derivative of the following expression:

(select all that apply)

• Constant rule

• Power rule

• Product rule

• Quotient rule

• Trig rule

 $f\left(x\right)=\sin^2\left(\cos x\right)$  

Find the derivative:

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

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

•  $2\sin x\cos\left(\sin x\right)\sin\left(\cos x\right)$  

•  $\sin x\cos\left(\cos x\right)\sin\left(\cos x\right)$  

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

Find $f'\left(x\right)$ :
 $f\left(x\right)=\cos\left(3x\sin\left(x^2\right)\right)$  

Select all components that are multiplied to make up the answer:

•  $\sin\left(3x\sin x^2\right)$  

•  $6x^2\cos\left(x^2\right)$  

•  $6x^2\cos\left(x^2\right)+3\sin\left(x^2\right)$  

•  $3\sin\left(x^2\right)$  

Explain the tangent line problem:

Tags

CCSS.HSA.REI.A.1

List the situations where a function is not differentiable:

(select all that apply)

• Discontinuity

• The function is a constant

• Vertical tangent line

• At a corner, cusp, abrupt angle