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Power Rule (Grades 11-12)

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Power Rule

1. 
Find the derivative. [math] f(x) = 3x^4 [/math]
  1. [math]f'(x) = 3x^3 [/math]
  2. [math]f'(x) = 12x [/math]
  3. [math]f'(x) = 12x^3 [/math]
  4. [math]f'(x) = 4x^3 [/math]
2. 
Differentiate. [math]f(x) = (4x^100)/25[/math]
  1. [math] f'(x) = (4x^99)/25[/math]
  2. [math] f'(x) = (8x^10) / 5 [/math]
  3. [math] f'(x) = x^99 / 625 [/math]
  4. [math] f'(x) = 16x^99[/math]
3. 
Differentiate. [math]f(x) = x^(-3/2) [/math]
  1. [math] f'(x) = x^(-5/2) [/math]
  2. [math]f'(x) = -3/2 x^(-5/2) [/math]
  3. [math]f'(x) = -3/2 x^(-1/2) [/math]
  4. [math] f'(x) = -2/3 x^(-2) [/math]
4. 
Find the derivative for this function: [math]f(x) = x^2 +5x+3[/math].
  1. [math]f'(x) = 2x+5[/math]
  2. [math] f'(x) = 2x+3[/math]
  3. [math]f'(x) = 2x+5x[/math]
5. 
What is the derivative of [math]f(x)=3x^3+2x^2[/math]?
  1. [math]f'(x)=9x^2+4x[/math]
  2. [math]f'(x)=3x^2+2x[/math]
  3. [math]f'(x)=0[/math]
  4. [math]f'(x)=12x^2+6x[/math]
6. 
Differentiate. [math] f(x) = 3x^-2 + 5x^-3 - 2x^-5 [/math]
  1. [math] f'(x) = -6x^-1 - 15x^-2 + 10x^-4 [/math]
  2. [math] f'(x) = 3x^-3 + 5x^-4 - 2x^-6 [/math]
  3. [math] f'(x) = 3x^-1 + 5x^-2 - 2x^-4 [/math]
  4. [math] f'(x) = -6x^-3 - 15x^-4 + 10x^-6 [/math]
7. 
Find the derivative. [math] f(x) = 2x^0.4 - 8x^(-0.02) [/math]
  1. [math] f'(x) = 2x^(-0.4) - 8x^(-1.02) [/math]
  2. [math] f'(x) = 0.8x^(-0.6) + 0.16x^(-1.02) [/math]
  3. [math] f'(x) = 2 + 0.16x^(-1.02) [/math]
  4. [math] f'(x) = 0.5x^(-0.6) + 0.4 x^(-1.02) [/math]
8. 
Find the derivative. [math] f(x) = root[5](x^7) [/math]
  1. [math] f'(x) = root[5](7x^6) [/math]
  2. [math] f'(x) = 7/5 root[5](x^2) [/math]
  3. [math] f'(x) = root[4](x^6) [/math]
  4. [math] f'(x) = root[5](x^2) [/math]
9. 
Find the derivative of the following function. [math] f(x) = 3x^5 - 10x^2 + 5x + 7 + 13/x - 3/x^3 [/math]
  1. [math] f'(x) = 15x^4 - 20x + 5 + 7/x - 9/x^4 [/math]
  2. [math] f'(x) = 15x^4 - 20x + 18 - 9/x^2[/math]
  3. [math] f'(x) = 15x^4 - 20x + 5 - 13/x^2 + 9/x^4 [/math]
  4. [math] f'(x) = 3x^3 - 23 - 3/x^2 [/math]
10. 
Differentiate. [math] f(x) = 3x^4 + 9sqrt(x) - 7/root[3](x^4) [/math]
  1. [math] f'(x) = 12x^3 + 9sqrt(x) + 7/(4root[3](x^3)) [/math]
  2. [math] f'(x) = 12x^3 + 9/2 sqrt(x) +21/(4root[3](x)) [/math]
  3. [math] f'(x) = 12x^3 + 9/(2sqrt(x)) + 28/(3root[3](x^7)) [/math]
  4. [math] f'(x) = 12x^3 +9 - 7/root[3](4x^3) [/math]
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