Advanced Differentiation Assessment Test

10 Questions | Total Attempts: 113

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Advanced Differentiation Assessment Test

In mathematics, differentiation is the process of finding the derivative, or rate of change, of a function. Take this assessment test to assess your knowledge of advanced differentiation.


Questions and Answers
  • 1. 
    What is the derivative of (y + 5) / (y2 – 1) with respect to y? 
    • A. 

      DF(y) = (-y2 – 10y – 1) / (y2 – 1)2

    • B. 

      DF(y) = (y2 + 10y – 1)

    • C. 

      DF(y) = (y2 – 1)2

    • D. 

      DF(y) = (-y2 –10x + 1) / (y2 – 1)2

  • 2. 
    Find dy/dx if y = 52x-1.
    • A. 

      52x-1 ln 10

    • B. 

      52x-1 ln 5

    • C. 

      52x-1 ln 25

    • D. 

      52x-1 ln 2

  • 3. 
    Differentiate ax2 + c to the ½ power. 
    • A. 

      2ax + c

    • B. 

      Ax + 2c

    • C. 

      2ax

    • D. 

      -2ax

  • 4. 
    Find the derivative of arcos 4x with respect to x. 
    • A. 

      -3/ [1 – (5x)^2]^2

    • B. 

      -4 /0.5

    • C. 

      [1 – (4x)^2]^0.5

    • D. 

      -4 / [(4x)^2 – 1]^0.5

  • 5. 
    Find the derivative of (y + 1)3 – y3 with respect to y. 
    • A. 

      6y – 3

    • B. 

      3y – 3

    • C. 

      6y+3

    • D. 

      3y+6

  • 6. 
    If there is a simple constant, what is the derivative of y = za?
    • A. 

      A za-1

    • B. 

      (a) - 2z

    • C. 

      Xa

    • D. 

      Ax

  • 7. 
    What is the derivative of ln (cos y)?
    • A. 

      Sec y

    • B. 

      –sec y

    • C. 

      –tan y

    • D. 

      Tan y

  • 8. 
    What is the second derivative of y by implicit differentiation from the equation 4×2 + 8y2 = 36.
    • A. 

      32xy

    • B. 

      64×2

    • C. 

      (– 9/4) y3

    • D. 

      (- 16/9) y3

  • 9. 
    What is the second derivative of this equation y3 – 5×2 + y = 0?
    • A. 

      10y – 5

    • B. 

      6y – 10

    • C. 

      3y + 10

    • D. 

      3×2 – 6y

  • 10. 
     What is the derivative of 4y?
    • A. 

      4 / (1 +16×2)0.5

    • B. 

      4 / (1 – 16×2)0.5

    • C. 

      4 / (1 + 4×2)0.5

    • D. 

      -4 / (1 - 4×2)0.5