10 Questions | Total Attempts: 124  Settings  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.

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• 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