Worksheets of Differential Calculus

Test your skills on Differential Calculus by trying out Differential Calculus worksheets. 10 Differential Calculus worksheets available to gain expertise and excel in your grades. The worksheets on Differential Calculus have been designed to offer a wide range of questions covering all details of the Differential Calculus and are in compliance with the k-12 curriculum. Detailed answers will be provided after you have attempted the Differential Calculus worksheet. Each worksheet will have around 10 questions and there are multiple worksheets available to try out.

Length of Polar Curve worksheet
1. Find the length of a = θ 0 ≤ θ ≤ 1?
  - ½ (√2 + (ln (1 + √2))
  - ½ (√2 + (1 + √2)
  - ½ (ln (1 + √2)
  - √2 + (1 + √2)
2. What is the length of the segment a = 6 / (1 + cos r ), 0 ≤ r ≤ ?
  - 6.000
  - 6.428
  - 7.248
  - 7.000
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Concavity and Points of Inflection Worksheet
1. Determine the concavity of f(x) = x³ –3x² −9x + 13 and identify any points of inflection of f(x)?
  - Concave downward on (−∞, 2) and concave upward on (2, + ∞), and function has a point of inflection at (0, 1)
  - Concave downward on (−∞, -1) and concave upward on (-1, + ∞), and function has a point of inflection at (0, 1)
  - Concave downward on (−∞, -1) and concave upward on (2, + ∞), and function has a point of inflection at (0, 1)
  - Concave downward on (−∞, 1) and concave upward on (1, + ∞), and function has a point of inflection at (0, 1)
2. Find the concavity of f(x) = x³ –6x² and identify any points of inflection of f(x)?
  - Concave downward on (−∞, 2) and concave upward on (2, + ∞), and function has a point of inflection at (2, 11)
  - Concave downward on (−∞, -1) and concave upward on (-1, + ∞), and function has a point of inflection at (2, 11)
  - Concave downward on (−∞, 2) and concave upward on (2, + ∞), and function has a point of inflection at (2, -16)
  - Concave downward on (−∞, 1) and concave upward on (1, + ∞), and function has a point of inflection at (0, 1)
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Product Rule Worksheet
1. Rewrite the following as single exponent using product rule, 4³ x 4 = ?
  - 256
  - -264
  - 265
  - 260
2. Evaluate y=(x²+2)(x+2), using product rule?
  - -x³+2x²+2x+4
  - x³+2x²+2x+4
  - x³+2x²+2x
  - x³+2x²+4
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Elementary Rules of Differentiation Worksheet
1. Solve d(x)/ dx, using elementary rule of differentiation?
  - 1
  - 2
  - 2x
  - x
2. Solve d(7x)/ dx, using elementary rule of differentiation?
  - 5
  - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»7«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/mrow»«mn»5«/mn»«/mfrac»«/math»$
  - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mi»x«/mi»«mn»7«/mn»«/mfrac»«/math»$
  - 7
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Area of Polar Curves Worksheet
1. Calculate the area of inner loop for the graph of r = 1+ 2cos θ?
  - π-(3√3)/2
  - π+6√3/2
  - -π-3/2
  - π-6√3
2. Find the area by one leaf of the rose for r = cos 2θ?
  - π+1/√2
  - π/4-1/√2
  - - π/4+4/√2
  - π/4+4/√2
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Slope of Polar Curves Worksheet
1. Identify the symmetries of the curve q = 4 + 4 cos Ɵ?
  - Symmetric at x-axis, not symmetric at y-axis and origin
  - Symmetric at x-axis, y-axis and origin
  - Not symmetric at x-axis, symmetric at y-axis and origin
  - Not symmetric at x-axis, y-axis and origin
2. Identify the symmetries of the curve s = 6 + sinƟ?
  - Symmetric at x-axis, not symmetric at y-axis and origin
  - Symmetric at x-axis, y-axis and origin
  - Not symmetric at x-axis, symmetric at y-axis and origin
  - Not symmetric at x-axis, y-axis and origin
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Inverse Function Rule Worksheet
1. Find the inverse of the function f(x) = (x-1)³ -7?
  - 1+3Ѵy-7
  - 1-3Ѵy-7
  - -1+3Ѵy-7
  - 3Ѵy-7
2. Find the inverse of the function f(x) = 3x+1?
  - (x – 1)/3
  - -(x – 1)/3
  - -1+3
  - (x + 1)/3
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Chain Rule Worksheet
1. Solve using Chain rule of differentiation?
  - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«msqrt»«mrow»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«mn»3«/mn»«/mrow»«/msqrt»«/mfrac»«/math»$
  - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«msqrt»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/mrow»«/msqrt»«/mfrac»«/math»$
  - - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mn»2«/mn»«msqrt»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»3«/mn»«mo»)«/mo»«/mrow»«/msqrt»«/mrow»«/mfrac»«/math»$
  - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»1«/mn»«mrow»«mn»2«/mn»«msqrt»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»3«/mn»«mo»)«/mo»«/mrow»«/msqrt»«/mrow»«/mfrac»«/math»$
2. Solve the problem using chain rule of differentiation , ?
  - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»26«/mn»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»5«/mn»«/mrow»«mrow»«mn»2«/mn»«msqrt»«mrow»«mn»13«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«mn»5«/mn»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»8«/mn»«/mrow»«/msqrt»«/mrow»«/mfrac»«/math»$
  - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»26«/mn»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»5«/mn»«/mrow»«mrow»«mn»2«/mn»«msqrt»«mrow»«mn»13«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»5«/mn»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»8«/mn»«/mrow»«/msqrt»«/mrow»«/mfrac»«/math»$
  - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»26«/mn»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»5«/mn»«/mrow»«mrow»«mn»2«/mn»«msqrt»«mrow»«mn»13«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»5«/mn»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«mn»8«/mn»«/mrow»«/msqrt»«/mrow»«/mfrac»«/math»$
  - $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»26«/mn»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«mn»5«/mn»«/mrow»«mrow»«mn»2«/mn»«msqrt»«mrow»«mn»13«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»5«/mn»«mi»x«/mi»«mo»§nbsp;«/mo»«mo»+«/mo»«mo»§nbsp;«/mo»«mn»8«/mn»«/mrow»«/msqrt»«/mrow»«/mfrac»«/math»$
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Differentiation is Linear Worksheet
1. Solve the linear differential equation x²dy/dx = -3y?
2. Find the solution of the given differential equation, dy / dx – y – xe^x = 0?
  - e^x{(x² / 2) + C}
  - e^2x{(x² / 2) + C}
  - e^x{(x / 2) + C}
  - e^-x{(x / 2) - C}
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Differential Formulas worksheet
1. Differentiate the following function with respect to x, f(x)=17 x100 – 5 x14 + 5x-4 – 46?
  - 1700 x⁹⁹ – 70 x¹³ – 20 x ^-3
  - 1700 x⁹⁹ – 70 x¹³ – 20 x ^-5
  - 1700 x⁹⁵ – 70 x¹³ – 20 x ^-5
  - 170 x⁹⁹ – 70 x¹² – 20 x ^-5
2. Find the differentiation of the function f (x) = x cos x?
  - x cos x + sin x
  - x cos x - sin x
  - cos x - x sin x
  - cos x + x sin x
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