Logarithmic differentiation

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Ari uses logarithmic differentiation on y = (x² + 1)ˣ. What is y′ at x = 1, to the nearest hundredth?

   3.39
2. 2.

   Bo uses logarithmic differentiation on y = x^(x²). What is y′ at x = 2, to the nearest hundredth?

   76.36
3. 3.

   Esme uses logarithmic differentiation on y = x^(x + 1). What is y′ at x = 2, to the nearest hundredth?

   17.55
4. 4.

   Jun uses logarithmic differentiation on y = (x + 1)^(2x). What is y′ at x = 1, to the nearest hundredth?

   9.55
5. 5.

   Kira uses logarithmic differentiation on y = (x + 1)²(x + 2)³/(x + 3)⁴. What is y′ at x = 1?

   27/64
6. 6.

   Milo uses logarithmic differentiation on y = (x + 3)²(x + 2)³/(x + 1)⁴. What is y′ at x = 1?

   -27/2
7. 7.

   Noah uses logarithmic differentiation on y = (x + 3)²(x + 1)³/(x + 2)⁴. What is y′ at x = 1?

   256/243
8. 8.

   Ren uses logarithmic differentiation on y = √x (x² + 1)³. Which is y′, with y the function itself?

   • y′ = 1/(2x) + 6x/(x² + 1)
   • y′ = y(1/x + 2x/(x² + 1))
   • y′ = y(1/(2x) + 6x/(x² + 1))
   • y′ = y(1/(2x) + 3/(x² + 1))
9. 9.

   Tala uses logarithmic differentiation on y = eˣ(x + 1)²/(x − 3)³. Which is y′, with y the function itself?

   • y′ = 1 + 2/(x + 1) − 3/(x − 3)
   • y′ = y(1 + 2/(x + 1) + 3/(x − 3))
   • y′ = y(1 + 1/(x + 1) − 1/(x − 3))
   • y′ = y(1 + 2/(x + 1) − 3/(x − 3))
10. 10.

    Zee uses logarithmic differentiation on y = (x² + 4)⁵ sin x. Which is y′, with y the function itself?

    • y′ = 10x/(x² + 4) + cos x/sin x
    • y′ = y(10x/(x² + 4) + cos x/sin x)
    • y′ = y(2x/(x² + 4) + cos x/sin x)
    • y′ = y(5/(x² + 4) + cos x/sin x)