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Derivatives Questions - All Grades

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Grade 12 Derivatives
Differentiate. [math]f(x) = 3x^5 - 2x^2 - 7x^(-3) + 9x^(-4)[/math]
  1. [math]f(x) = 15x^4 - 4x - 21x^(-2) + 36x^(-3)[/math]
  2. [math]f(x) = 15x^4 - 4x + 21x^(-4) - 36x^(-5)[/math]
  3. [math]f(x) = 15x^4 - 4x + 21x^(2) - 36x^(5)[/math]
  4. [math]f(x) = 15x^4 - 4x - 21x^(-4) + 36x^(-5)[/math]
Grade 12 Derivatives
What is the derivative of [math]f(x) = 2sqrt(x^7) - 5root[4](x^3) + 9root[3](x^2) - 6/root[6](x^5)?[/math]
  1. [math]f'(x) = x^3 - 5/2 sqrt(x) + 9/2root[6](x) + 3/root[3](x^4)[/math]
  2. [math]f'(x) = 7sqrt(x^5) - 20/(3root[4](x)) + 3/(2root[3](x)) - 5/root[6](x^11)[/math]
  3. [math]f'(x) = 7sqrt(x^5) - 15/(4root[4](x)) + 6/root[3](x) + 5/root[6](x^11)[/math]
  4. [math]f'(x) = 14x^3 - 15sqrt(x)+ 18root[3](x) + 30/root[3](x^2)[/math]
Grade 12 Derivatives
Find the derivative. [math]f(x) = 4x^3 - 3sqrt(x^3) + sqrt(x)[/math]
  1. [math]f'(x) = 12x^2 - 9/2 sqrt(x) + 1/(2sqrt(x))[/math]
  2. [math]f'(x) = 12x^2 + 2/(sqrt(x))[/math]
  3. [math]f'(x) = 4x^2 - 9sqrt(x) + 1[/math]
  4. [math]f'(x) = 64x^2 + 9sqrt(x) - 1/sqrt(x)[/math]
Grade 12 Derivatives
Find the derivative. [math]f(x) = 4sqrt(x)+3[/math]
  1. [math]f'(x) = 4/sqrt(x)[/math]
  2. [math]f'(x) = 4/sqrt(x) + 1/3[/math]
  3. [math]f'(x) = 2[/math]
  4. [math]f'(x) = 2/sqrt(x)[/math]
Grade 12 Derivatives
What is the derivative of [math]f(x)=23pi ?[/math]
  1. [math]f'(x) = 23pi[/math]
  2. [math]f'(x) = pi[/math]
  3. [math]f'(x) = 0[/math]
  4. [math] f'(x) = 23[/math]
Grade 12 Derivatives
Differentiate. [math]f(x)=2x^6[/math]
  1. [math]f'(x) = 6[/math]
  2. [math]f'(x) = 6x^5[/math]
  3. [math]f'(x) = 12x^5[/math]
  4. [math]f'(x) = 12[/math]
Grade 12 Derivatives
What is the derivative of [math]f(x) = 3x^2 - x + 8 ?[/math]
  1. [math]f'(x)=6x-1[/math]
  2. [math]f'(x)=6x+8[/math]
  3. [math]f'(x) = 3x[/math]
  4. [math]f'(x)=9x+7[/math]
Grade 12 Derivatives
What is the derivative of [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[/math]
Grade 12 Derivatives
Find the derivative. [math]f(x)=5x^2−6x+4[/math]
  1. [math]f'(x) = 10x - 6[/math]
  2. [math]f'(x) = 5x - 6[/math]
  3. [math]f'(x) = 25x[/math]
  4. [math]f'(x) = 7x - 5[/math]
Grade 12 Derivatives
Find the derivative. [math]f(x)=99x[/math]
  1. [math]f'(x) = 99[/math]
  2. [math]f'(x) = x[/math]
  3. [math]f'(x) = 99x[/math]
  4. [math]f'(x) = 100[/math]
Grade 12 Derivatives
Calculate the derivative. [math]f(x)=8x^2-5x+3[/math]
  1. [math]f'(x) = 8x[/math]
  2. [math]f'(x) = 16x-5x[/math]
  3. [math]f'(x) = 2x-5[/math]
  4. [math]f'(x) = 16x-5[/math]
Grade 12 Derivatives
What is the derivative of [math]f(x)=sin(3x^2) ?[/math]
  1. [math]f'(x)=3x^2cos(3x^2)[/math]
  2. [math]f'(x)=6xcos(3x^2)[/math]
  3. [math]f'(x)=3x^2sin(3x^2)[/math]
  4. [math]f'(x)=6xsin(3x^2)[/math]
Grade 12 Derivatives
On what intervals is the function [math]f(x)=3x^3+2x^2[/math] concave upwards and downwards?
  1. concave upward [math](-2/9, oo)[/math], concave downward [math](-oo, -2/9)[/math]
  2. concave upward [math](-oo, -2/9)[/math], concave downward [math](-2/9, oo)[/math]
  3. concave upward [math](0, oo)[/math], concave downward [math](-oo, 0)[/math]
  4. concave upward [math](-oo, 0)[/math], concave downward [math](0, oo)[/math]
Grade 12 Derivatives
What is the second derivative of [math]f(x)=3x^3+2x^2[/math]?
  1. [math]f''(x)=18x+4[/math]
  2. [math]f''(x)=9x^2+4x[/math]
  3. [math]f''(x)=18[/math]
  4. [math]f''(x)=0[/math]
Grade 12 Derivatives
Identify the intervals on which the given function is increasing and decreasing.
[math]f(x)=x^3+x^2-x[/math]
  1. Increasing: [math](-oo, -1) uu (1/3,oo)[/math]; decreasing: [math](-1, 1/3) [/math]
  2. Increasing: [math](-oo, -1)[/math]; decreasing: [math](-1, 1/3)[/math]
  3. Increasing for all x
  4. Increasing: [math](-1,1/3)[/math]; decreasing: [math](-oo, -1) uu (1/3,oo)[/math]
Grade 12 Derivatives
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]
Grade 12 Derivatives
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]
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