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Derivatives Questions - All Grades

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Grade 12 Derivatives
Differentiate. f(x)=3x5-2x2-7x-3+9x-4
  1. f(x)=15x4-4x-21x-2+36x-3
  2. f(x)=15x4-4x+21x-4-36x-5
  3. f(x)=15x4-4x+21x2-36x5
  4. f(x)=15x4-4x-21x-4+36x-5
Grade 12 Derivatives
What is the derivative of f(x)=3x2-x+8?
  1. f′(x)=6x-1
  2. f′(x)=6x+8
  3. f′(x)=3x
  4. f′(x)=9x+7
Grade 12 Derivatives
What is the derivative of f(x)=23π?
  1. f′(x)=23π
  2. f′(x)=π
  3. f′(x)=0
  4. f′(x)=23
Grade 12 Derivatives
What is the derivative of f(x)=2√x7-54√x3+93√x2-66√x5?
  1. f′(x)=x3-52√x+926√x+33√x4
  2. f′(x)=7√x5-2034√x+323√x-56√x11
  3. f′(x)=7√x5-1544√x+63√x+56√x11
  4. f′(x)=14x3-15√x+183√x+303√x2
Grade 12 Derivatives
What is the derivative of f(x)=3x4?
  1. f′(x)=3x3
  2. f′(x)=12x
  3. f′(x)=12x3
  4. f′(x)=4x
Grade 12 Derivatives
Find the derivative. f(x)=4√x+3
  1. f′(x)=4√x
  2. f′(x)=4√x+13
  3. f′(x)=2
  4. f′(x)=2√x
Grade 12 Derivatives
On what intervals is the function f(x)=3x3+2x2 concave upwards and downwards?
  1. concave upward (-29,∞), concave downward (-∞,-29)
  2. concave upward (-∞,-29), concave downward (-29,∞)
  3. concave upward (0,∞), concave downward (-∞,0)
  4. concave upward (-∞,0), concave downward (0,∞)
Grade 12 Derivatives
Find the derivative. f(x)=99x
  1. f′(x)=99
  2. f′(x)=x
  3. f′(x)=99x
  4. f′(x)=100
Grade 12 Derivatives
Differentiate. f(x)=2x6
  1. f′(x)=6
  2. f′(x)=6x5
  3. f′(x)=12x5
  4. f′(x)=12
Grade 12 Derivatives
Calculate the derivative. f(x)=8x2-5x+3
  1. f′(x)=8x
  2. f′(x)=16x-5x
  3. f′(x)=2x-5
  4. f′(x)=16x-5
Grade 12 Derivatives
Find the derivative. f(x)=4x3-3√x3+√x
  1. f′(x)=12x2-92√x+12√x
  2. f′(x)=12x2+2√x
  3. f′(x)=4x2-9√x+1
  4. f′(x)=64x2+9√x-1√x
Grade 12 Derivatives
What is the derivative of f(x)=sin(3x2)?
  1. f′(x)=3x2cos(3x2)
  2. f′(x)=6xcos(3x2)
  3. f′(x)=3x2sin(3x2)
  4. f′(x)=6xsin(3x2)
Grade 12 Derivatives
What is the second derivative of f(x)=3x3+2x2?
  1. f′′(x)=18x+4
  2. f′′(x)=9x2+4x
  3. f′′(x)=18
  4. f′′(x)=0
Grade 12 Derivatives
Find the derivative. f(x)=5x2−6x+4
  1. f′(x)=10x-6
  2. f′(x)=5x-6
  3. f′(x)=25x
  4. f′(x)=7x-5
Grade 12 Derivatives
Identify the intervals on which the given function is increasing and decreasing.
f(x)=x3+x2-x
  1. Increasing: (-∞,-1)∪(13,∞); decreasing: (-1,13)
  2. Increasing: (-∞,-1); decreasing: (-1,13)
  3. Increasing for all x
  4. Increasing: (-1,13); decreasing: (-∞,-1)∪(13,∞)
Grade 12 Derivatives
On f(x)=2x5+x3-3x
  1. (-0.65,1.4) is a relative and absolute maximum.
  2. (0.65,-1.4) is a relative and absolute minimum.
  3. (-0.65,1.4) is a relative maximum.
  4. (0.65,-1.4) is a relative minimum.
  5. Both A and B.
  6. Both C and D.
  7. None of the above.
Grade 12 Derivatives
What is the derivative of f(x)=3x3+2x2?
  1. f′(x)=9x2+4x
  2. f′(x)=3x2+2x
  3. f′(x)=0
  4. f′(x)=12x2+6x
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