Grade 12 · Math · Calculus

12th grade Logarithmic differentiation worksheet

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Logarithmic differentiation

Grade 12 Math Worksheet

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1.
Ari uses logarithmic differentiation on y = x^(sin x). Which is y′?
- y′ = sin x · x^(sin x − 1)
- y′ = x^(sin x)(cos x ln x + (sin x)/x)
- y′ = cos x ln x + (sin x)/x
- y′ = x^(sin x) cos x ln x
2.
Bo uses logarithmic differentiation on y = x^(eˣ). Which is y′?
- y′ = eˣ ln x + eˣ/x
- y′ = x^(eˣ) eˣ ln x
- y′ = x^(eˣ)(eˣ ln x + eˣ/x)
- y′ = eˣ · x^(eˣ − 1)
3.
Esme uses logarithmic differentiation on y = (x² + 1)ˣ. Which is y′?
- y′ = (x² + 1)ˣ(ln(x² + 1) + 2x²/(x² + 1))
- y′ = 2x² (x² + 1)^(x − 1)
- y′ = (x² + 1)ˣ ln(x² + 1)
- y′ = ln(x² + 1) + 2x²/(x² + 1)
4.
Jun uses logarithmic differentiation on y = x^(√x). Which is y′?
- y′ = x^(√x) ln x/(2√x)
- y′ = ln x/(2√x) + 1/√x
- y′ = x^(√x)(ln x/(2√x) + 1/√x)
- y′ = √x · x^(√x − 1)
Luz uses logarithmic differentiation on y = (x + 3)²/(x + 1)². What is y′ at x = 1?
Milo uses logarithmic differentiation on y = (x − 1)⁴/(x + 1)². What is y′ at x = 2?
Noah uses logarithmic differentiation on y = (x + 2)³/(x + 1)³. What is y′ at x = 0?
Ren uses logarithmic differentiation on y = x²√(x − 1). What is y′ at x = 2?
Tala uses logarithmic differentiation on y = x²√(x + 3). What is y′ at x = 1?
Zee uses logarithmic differentiation on y = x²√(x + 7). 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.

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