Worksheets of Differentiation Formulas

Test your skills on Differentiation Formulas by trying out Differentiation Formulas worksheets. 7 Differentiation Formulas worksheets available to gain expertise and excel in your grades. The worksheets on Differentiation Formulas have been designed to offer a wide range of questions covering all details of the Differentiation Formulas and are in compliance with the k-12 curriculum. Detailed answers will be provided after you have attempted the Differentiation Formulas worksheet. Each worksheet will have around 10 questions and there are multiple worksheets available to try out.

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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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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