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mathematics UK Year 12 Mathematics (AS)
 
Solved problems for the chapter:
 

The Quotient Rule For Derivatives

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:the_quotient_rule_for_derivatives/4807/


Example 1.

Calculate the derivative of the function:


    
Example 2.

Find the derivative of the function:


    
3.

Given the function:




Find the value of .

    
4.

Find the differential coefficient of the tangent to the graph:




at point x = 2.

    
5.

Find the derivative of the function:


    
6.

Find the derivative of the function:


    
7.

Find the derivative of the function:


    
8.

Given the function:




calculate the value of .

    

9.

Find the derivative of the function:


    
10.

Find the derivative of the function:


    
11.

Find the derivative of the function:


    
12.

Find the derivative of the function:


    
13.

Given the function f:


.


  • Draw the graph of the function

  • Write the intersections of the graph with the coordinate axes

  • Write the equations of the vertical and horizontal asymptotes.

  • Prove computationally that the function f has no stationary points.


    
14.

Given the function f as:




  • Calculate the zero of the function f.


  • Calculate the poles of the function f.


  • Obtain the equation of the horizontal asymptote of the graph of the function f.


  • Calculate the derivative of the function f.


  • Draw the graph of the function in the given coordinate system.