Advanced Derivatives Assessment Test

10 Questions | Total Attempts: 124

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Advanced Derivatives Assessment Test

Applying the common derivative rules in more elaborate ways is what advanced derivatives mean. Take this assessment test to evaluate your knowledge of this topic.


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

    • B. 

      2ax

    • C. 

      2ax + c

    • D. 

      Ax + 2c

  • 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 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 arccos 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