Grade 12 · Math · Calculus

12th grade Logarithmic differentiation worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

Logarithmic differentiation

Grade 12 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Ari takes ln of both sides of y = xˣ to find y′. What is y′ at x = 2, to the nearest hundredth?
Bo takes ln of both sides of y = xˣ to find y′. What is y′ at x = 3, to the nearest hundredth?
Esme takes ln of both sides of y = xˣ to find y′. What is y′ at x = 1.5, to the nearest hundredth?
Jun takes ln of both sides of y = xˣ to find y′. What is y′ at x = 0.5, to the nearest hundredth?
5.
Kira starts logarithmic differentiation on y = xˣ. Which first step is right?
- ln y = ln x · ln x
- ln y = x + ln x
- y = x ln x
- ln y = x ln x
6.
Luz starts logarithmic differentiation on y = (x² + 1)³(x − 4)². Which first step is right?
- ln y = 3 ln(x² + 1) + 2 ln(x − 4)
- ln y = ln(x² + 1) + ln(x − 4)
- ln y = 6 ln(x² + 1) ln(x − 4)
- y = 3 ln(x² + 1) + 2 ln(x − 4)
7.
Milo starts logarithmic differentiation on y = (sin x)ˣ. Which first step is right?
- y = x ln(sin x)
- ln y = ln x · ln(sin x)
- ln y = x ln(sin x)
- ln y = x + ln(sin x)
8.
Noah starts logarithmic differentiation on y = x⁴(x + 1)⁵. Which first step is right?
- y = 4 ln x + 5 ln(x + 1)
- ln y = ln x + ln(x + 1)
- ln y = 20 ln x ln(x + 1)
- ln y = 4 ln x + 5 ln(x + 1)
Ren uses logarithmic differentiation on y = (x + 2)²(x − 1)³. What is y′ at x = 2?
Zee uses logarithmic differentiation on y = (x − 1)²(x + 1)². What is y′ at x = 2?

Logarithmic differentiation. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

logarithmic differentiation: Take ln of both sides, differentiate, then multiply by y.

variable power: A power that depends on x, as in xˣ.

y′/y: What differentiating ln y gives; multiply by y for y′.

Used the power rule on a function whose power changes. Take ln of both sides first.

Used the aˣ rule on a function whose base changes too. The product rule on ln y adds a second term.

Stopped at y′/y. Multiply by y to get y′.

What is the most common mistake with logarithmic differentiation?

Used the power rule on a function whose power changes. Take ln of both sides first.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records