Problems about Limits and Differentiation of functions




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These exercises are based on the theory treated on the pages
Limits of functions (part I)
The derivative, differentiation, limits (part II), maximum, minimum, inflection points

If a problem is solved. It is not 'the' answer.
No attempt is made to search for the most elegant answer.
I highly recommend that you at least try to solve the problem before you read the solution.

Problems about Differentiation of functions and limits

Level 1 problems

 
y = 5x  ;  y' = 5

y = x3  ;  y' = 3x2

y = (2x2+ x + 5)  ;  y'= 4x + 1

     x - 1            (x+1).1 - (x-1).1             2
y = ------- ;   y' = -------------------- = ------------------
     x + 1              (x+1)(x+1)              (x+1)(x+1)

y = (x+5)6  ;  y' = 6.(x+5)5


y = (2x + 6)3 ; y' = 3.(2x + 6)2.2

y =  (2x + 6)(5x - 7) ; y'= 2.(5x - 7) + (2x + 6).5

y =  (2x + 6)2.(5x - 7)3; y'= 2.(2x + 6).2.(5x - 7)3+ (2x + 6)2.3.(5x - 7)2.5

y = x/5  ; y' = 1/5

                    1
y = 5/x  ; y' = -5.---
                   x.x

     7
y = ---  <=> y = 7.x-4  ;   y' = -28 x-5
    x4

Level 2 problems

Level 3 problems


External links to solved problems on differentiation

Chain Rule

Exercises on the chain rule

Product rule

Exercises on the product rule

Quotient rule

Exercises on the quotient rule

Trigonometric functions

Exercises on differentiation of trigonometric functions

Cyclometric functions

Exercises on differentiation of cyclometric functions

Implicit differentiation

Exercises on implicit differentiation

Functions uv

Exercises on differentiation of functions uv





Topics and Problems

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