Grade 12 · Math · Calculus

12th grade Inverse function rule and inverse trig derivatives worksheet

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Inverse function rule and inverse trig derivatives

Grade 12 Math Worksheet - Building Confidence

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At x = 2, 5 and 4; at x = 5, 9 and 3. f has an inverse g. Ari uses the table shown. What is g′(5)?
At x = 1, 3 and 6; at x = 3, 10 and 2. f has an inverse g. Bo uses the table shown. What is g′(3)?
At x = 3, 8 and 5; at x = 8, 1 and -4. f has an inverse g. Jun uses the table shown. What is g′(8)?
4.
Kira differentiates f(x) = 3 arcsin x. Which is f′(x)?
- f′(x) = 3/√(1 + x²)
- f′(x) = 3/√(1 − x²)
- f′(x) = −3/√(1 − x²)
- f′(x) = 3/(1 + x²)
5.
Luz differentiates f(x) = 2 arccos x. Which is f′(x)?
- f′(x) = −2/√(1 + x²)
- f′(x) = −2/(1 + x²)
- f′(x) = −2/√(1 − x²)
- f′(x) = 2/√(1 − x²)
6.
Noah differentiates f(x) = 4 arccos x. Which is f′(x)?
- f′(x) = −4/(1 + x²)
- f′(x) = −4/√(1 − x²)
- f′(x) = 4/√(1 − x²)
- f′(x) = −4/√(1 + x²)
Pia differentiates f(x) = 10 arctan x. What is f′(3)?
Ren differentiates f(x) = 15 arctan x. What is f′(2)?
Tala differentiates f(x) = 8 arctan x. What is f′(-3)?
Zee differentiates f(x) = 34 arctan x. What is f′(4)?

Inverse function and inverse trig derivatives. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

inverse g: The function that undoes f: g(f(x)) = x.

g′(b) = 1/f′(a): The inverse's slope at b, where f(a) = b.

arctan: The angle whose tangent is x.

Gave f′(a) instead of its reciprocal. Mirroring a graph in y = x flips rise and run, so g′(b) = 1/f′(a).

Read f′ at b instead of at a, the x where f(a) = b.

Used the wrong sign. Only arccos has a negative derivative; arcsin and arctan rise.

What is the most common mistake with inverse function rule and inverse trig derivatives?

Gave f′(a) instead of its reciprocal. Mirroring a graph in y = x flips rise and run, so g′(b) = 1/f′(a).

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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