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Derivatives Questions - All Grades

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Grade 12 Derivatives
Find the derivative. f(x)=2x0.4-8x-0.02
  1. f′(x)=2x-0.4-8x-1.02
  2. f′(x)=0.8x-0.6+0.16x-1.02
  3. f′(x)=2+0.16x-1.02
  4. f′(x)=0.5x-0.6+0.4x-1.02
Grade 12 Derivatives
Find the derivative. f(x)=5√x7
  1. f′(x)=5√7x6
  2. f′(x)=755√x2
  3. f′(x)=4√x6
  4. f′(x)=5√x2
Grade 12 Derivatives
Differentiate. f(x)=4x10025
  1. f′(x)=4x9925
  2. f′(x)=8x105
  3. f′(x)=x99625
  4. f′(x)=16x99
Grade 12 Derivatives
On what intervals is the function f(x)=3x3+2x2 increasing or decreasing?
  1. Increasing: (-∞,-49)∪(0,∞), decreasing: (-49,0)
  2. Increasing: (-∞,-49), decreasing: (-49,0)
  3. Increasing: (-∞,0)∪(-49,∞), decreasing: (-49,0)
  4. Increasing: (-49,0), decreasing: (-∞,-49)∪(0,∞)
Grade 12 Derivatives
Find the intervals of increase and decrease for the following function. f(x)=√3x2-9x+6
  1. Increasing on (32,∞) and decreasing on (-∞,32)
  2. Increasing on (2,∞) and decreasing on (-∞,1)
  3. Increasing on (32,∞)
  4. Increasing on (2,∞)
Grade 12 Derivatives
What are all the values of x for which the function f defined by f(x)=x3+3x2-9x+7 is increasing?
  1. -3<x<1
  2. -1<x<1
  3. x<-3 and x>1
  4. x<-1 and x>3
  5. All real numbers
Grade 12 Derivatives
Identify the intervals on which the given function is increasing and decreasing.
f(x)=x2e-x2
  1. Increasing: (-∞,-1)∪(0,1); decreasing: (-1,0)∪(1,∞)
  2. Increasing: (-∞,0); decreasing: (0,∞)
  3. Increasing for all x
  4. Increasing: (-1,0)∪(1,∞); decreasing: (-∞,-1)∪(0,1)
Grade 12 Derivatives
Find ddx(tan-1(x-√a2-x2x+√a2-x2)).
  1. -1√a2-x2
  2. 1√a2-x2
  3. √a2-x2
  4. x√a2-x2
College Derivatives
What is the derivative of 21?
  1. 0
  2. 21
  3. 7
  4. 3
Grade 12 Derivatives
What are the critical numbers of the following equation?
f(x)=3x3+2x2
  1. x=-49,0
  2. x=49,0
  3. x=-94,0
  4. x=94,0
Grade 12 Derivatives
Identify and classify the extrema of the given function.
f(x)=x3+x2-x
  1. Relative maximum: (-1,32); relative minimum: (13,-1)
  2. Relative maximum: (-1,1); absolute minimum: (13,-527)
  3. Relative maximum: (-1,1); relative minimum: (13,-527)
  4. Relative maximum: (-1,32); no relative or absolute minimums
Grade 12 Derivatives
An equation of the line tangent to the graph of y=cos(2x) at x=π4 is which of the following?
  1. y-1=-(x-π4)
  2. y-1=-2(x-π4)
  3. y=2(x-π4)
  4. y=-(x-π4)
  5. y=-2(x-π4)
Grade 12 Derivatives
f(x)=2x5+x3-3x is
  1. increasing on (-∞,∞).
  2. decreasing on (-∞,-0.65)∪(0.65,∞) and increasing on (-0.65,0.65).
  3. increasing on (-∞,-0.65)∪(0.65,∞) and decreasing on (-0.65,0.65).
  4. decreasing on (-∞,-1.4)∪(1.4,∞) and decreasing on (1.4,-1.4).
Grade 12 Derivatives
Find the derivative for this function: f(x)=x2+5x+3.
  1. f′(x)=2x+5
  2. f′(x)=2x+3
  3. f′(x)=2x+5x
Grade 12 Derivatives
Differentiate. f(x)=x-32
  1. f′(x)=x-52
  2. f′(x)=-32x-52
  3. f′(x)=-32x-12
  4. f′(x)=-23x-2
Grade 12 Derivatives
Differentiate. f(x)=3x-2+5x-3-2x-5
  1. f′(x)=-6x-1-15x-2+10x-4
  2. f′(x)=3x-3+5x-4-2x-6
  3. f′(x)=3x-1+5x-2-2x-4
  4. f′(x)=-6x-3-15x-4+10x-6
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