Logarithmic differentiation

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari takes ln of both sides of y = xˣ to find y′. What is y′ at x = 2, to the nearest hundredth?

   6.77
2. 2.

   Bo takes ln of both sides of y = xˣ to find y′. What is y′ at x = 3, to the nearest hundredth?

   56.66
3. 3.

   Esme takes ln of both sides of y = xˣ to find y′. What is y′ at x = 1.5, to the nearest hundredth?

   2.58
4. 4.

   Jun takes ln of both sides of y = xˣ to find y′. What is y′ at x = 0.5, to the nearest hundredth?

   0.22
5. 5.

   Kira starts logarithmic differentiation on y = xˣ. Which first step is right?

   • ln y = x + ln x
   • y = x ln x
   • ln y = x ln x
   • ln y = ln x · ln x
6. 6.

   Luz starts logarithmic differentiation on y = (x² + 1)³(x − 4)². Which first step is right?

   • y = 3 ln(x² + 1) + 2 ln(x − 4)
   • ln y = 3 ln(x² + 1) + 2 ln(x − 4)
   • ln y = 6 ln(x² + 1) ln(x − 4)
   • ln y = ln(x² + 1) + ln(x − 4)
7. 7.

   Milo starts logarithmic differentiation on y = (sin x)ˣ. Which first step is right?

   • ln y = ln x · ln(sin x)
   • y = x ln(sin x)
   • ln y = x ln(sin x)
   • ln y = x + ln(sin x)
8. 8.

   Noah starts logarithmic differentiation on y = x⁴(x + 1)⁵. Which first step is right?

   • ln y = 4 ln x + 5 ln(x + 1)
   • ln y = ln x + ln(x + 1)
   • ln y = 20 ln x ln(x + 1)
   • y = 4 ln x + 5 ln(x + 1)
9. 9.

   Ren uses logarithmic differentiation on y = (x + 2)²(x − 1)³. What is y′ at x = 2?

   56
10. 10.

    Zee uses logarithmic differentiation on y = (x − 1)²(x + 1)². What is y′ at x = 2?

    24