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Twelfth Grade (Grade 12) Derivatives Questions

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Grade 12 Derivatives
Find the derivative of the following function. f(x)=3x5-10x2+5x+7+13x-3x3
  1. f′(x)=15x4-20x+5+7x-9x4
  2. f′(x)=15x4-20x+18-9x2
  3. f′(x)=15x4-20x+5-13x2+9x4
  4. f′(x)=3x3-23-3x2
Grade 12 Derivatives
Find the derivative. f(x)=3x4
  1. f′(x)=3x3
  2. f′(x)=12x
  3. f′(x)=12x3
  4. f′(x)=4x3
Grade 12 Derivatives
Differentiate. f(x)=3x4+9√x-73√x4
  1. f′(x)=12x3+9√x+743√x3
  2. f′(x)=12x3+92√x+2143√x
  3. f′(x)=12x3+92√x+2833√x7
  4. f′(x)=12x3+9-73√4x3
Grade 12 Derivatives
What is ddx(xlnx)?
  1. xlnx
  2. (lnx)x
  3. (2x)(lnx)(xlnx)
  4. (lnx)(xlnx-1)
  5. 2(lnx)(xlnx)
Grade 12 Derivatives
Find dydxify=3x23-4x12-2.
  1. 2x13-2x-12
  2. 3x-13-2x-12
  3. 95x53-8x32+C
  4. 2x-13-2x-12
Grade 12 Derivatives
Find f′(x) if f(x)=sinxcotx.
  1. cos x
  2. -sin x
  3. sin x
  4. -cos x
  5. 0
Grade 12 Derivatives
If f(x)=lnxx, for all x>0, which of the following is true?
  1. f is increasing for all x greater than 0
  2. f is increasing for all x greater than 1
  3. f is decreasing for all x between 0 and 1
  4. f is decreasing for all x between 1 and e
  5. f is decreasing for all x greater than e
Grade 12 Derivatives
Find ddx(lne2x).
  1. 1e2x
  2. 2e2x
  3. 2x
  4. 1
  5. 2
Grade 12 Derivatives
Find dydx if ycosx=1.
  1. ysinx
  2. ytanx
  3. ycosx
  4. ycotx
Grade 12 Derivatives
If x2+y2=81, find dydx.
  1. -81xy
  2. -xy
  3. -81yx
  4. -yx
Grade 12 Derivatives
If sin(x+y)=log(x+y) then dydx=
  1. tan(x+y)
  2. log[tan(x+y)]
  3. -1
  4. 1
Grade 12 Derivatives
What is limh→0cos(π3+h)-cos(π3)h?
  1. 0
  2. 12
  3. √32
  4. -√32
Grade 12 Derivatives
Determine the intervals of increase and decrease. f(x)=x2x2-1
  1. Increasing on (-∞,0) and decreasing on (0,∞)
  2. Increasing on (-√2,0)∪(√2,∞) and decreasing on (-∞,-√2)∪(0,√2)
  3. Increasing on (-∞,-1)∪(1,∞) and decreasing on (-1,1)
  4. Increasing on (-∞,-1)∪(-1,0) and decreasing on (0,1)∪(1,∞)
Grade 12 Derivatives
If y=x2ex, then dydx=
  1. 2xex
  2. x(x+2ex)
  3. xex(x+2)
  4. 2x+ex
  5. 2x+e
Grade 12 Derivatives
If y=x5cosx, find d2ydx2.
  1. -20x3cosx
  2. 20x3cosx-x5cosx
  3. 20x3cosx-10x4sinx-x5cosx
  4. 20x3cosx+x5cosx
  5. 20x3
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