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Calculus practice

Differentiation Tables worksheets

Apply sum, difference, product, quotient, scalar and Chain Rules to exact function and derivative values in one shared lookup table.

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Use the shared table to choose the required values, apply the derivative rule and give a reduced exact answer.

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Choose values before calculating

Each row supplies f, f', g and g' at one input. Write the derivative rule first, then substitute only the values that rule needs.

Learning objective

What this activity builds

Use tabulated function and derivative values to evaluate derivatives exactly.

Worked example

If h(x) = f(g(x)), what values are needed for h'(a)?

Use f'(g(a)) and g'(a), then multiply.

First read g(a), move to the row whose input equals that value to find f'(g(a)), then multiply by g'(a).

Teaching notes

Make the practice count

  • Name the derivative rule before substituting table values.
  • For composition, use the outer-function row at g(a), not the row at a.
  • For quotients, verify the denominator value is nonzero.

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Choose 6 or 12 problems, one or more difficulty groups, and x-only or mixed variables. Every six-problem page repeats the same lookup table.

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Math SheetNameScoreTeacherDateDifferentiation TablesUse the shared table to apply derivative rules and find each exact derivative value.Each row gives function and derivative values at the displayed input. f and g are differentiable at every required input.inputff'gg'-55446-4-902-6-1-1-4-50004-112720-546-3-431.h(x) = (f(x))^2Find h'(0).2.h(x) = (f(x))^2Find h'(-5).3.h(x) = (f(x))/(g(x))Find h'(0).4.h(x) = f(g(x))Find h'(-1).5.h(x) = -3f(x) + 5g(x)Find h'(-1).6.h(x) = f(x) - g(x)Find h'(-5).math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateDifferentiation TablesUse the shared table to apply derivative rules and find each exact derivative value.Each row gives function and derivative values at the displayed input. f and g are differentiable at every required input.inputff'gg'-55446-4-902-6-1-1-4-50004-112720-546-3-437.h(x) = (5f(x))(-3g(x))Find h'(-1).8.h(x) = (f(x))(g(x))Find h'(2).9.h(x) = -3f(x) + 4g(x)Find h'(-4).10.h(x) = f(g(x))Find h'(0).11.h(x) = f(x) + g(x)Find h'(4).12.h(x) = (5f(x))/(-4g(x))Find h'(-4).math-sheet.comPage 2 of 2

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