Derivatives worksheet with answers

Free printable Derivatives worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xyx = 1

Let f(x) = x5 + 5x2 + 4x − 7. Find the slope of the graph at x = 1, that is f′(1).

f(x) = x5 + 5x2 + 4x − 7x = 1
f′(1) =
2.Easy
xyx = 3

Let f(x) = −x3 + 7x2 + 8x − 3. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −x3 + 7x2 + 8x − 3x = 3
f′(3) =
3.Medium
xyx = 1.5

Let f(x) = x2·e−0.5x. Find f′(1.5).

f(x) = x2·e−0.5xx = 1.5
f′(1.5) =
4.Medium
xyx = −2

Let f(x) = ln(x2 + 1). Find f′(−2).

f(x) = ln(x2 + 1)x = −2
f′(−2) =
5.Hard
xy

Let f(x) = x3 − 4.5x2 + 6x − 4. Find the x-coordinate x of the local maximum.

f(x) = x3 − 4.5x2 + 6x − 4
x =
6.Hard
xyx = −2

The tangent line to f(x) = 0.5x2 − 5x − 2 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 5x − 2x = −2
b =

Answer key

  1. 1. f′(1) = 19
  2. 2. f′(3) = 23
  3. 3. f′(1.5) = 0.8857
  4. 4. f′(−2) = −0.8
  5. 5. x = 1
  6. 6. b = −4

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