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 = 3

Let f(x) = 5x3 + 7x2 + x − 4. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 5x3 + 7x2 + x − 4x = 3
f′(3) =
2.Easy
xyx = 1

Let f(x) = −4x3 + 7x2 + x + 8. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x3 + 7x2 + x + 8x = 1
f′(1) =
3.Medium
xyx = 1

Let f(x) = x·e0.5x. Find f′(1).

f(x) = x·e0.5xx = 1
f′(1) =
4.Medium
xyx = 0.5

Let f(x) = x3·e−0.5x. Find f′(0.5).

f(x) = x3·e−0.5xx = 0.5
f′(0.5) =
5.Hard
xy

Let f(x) = x3 − 15x2 + 63x + 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 15x2 + 63x + 5
x =
6.Hard
xyx = 2

The tangent line to f(x) = x2 + 4x − 6 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = x2 + 4x − 6x = 2
b =

Answer key

  1. 1. f′(3) = 178
  2. 2. f′(1) = 3
  3. 3. f′(1) = 2.473
  4. 4. f′(0.5) = 0.5354
  5. 5. x = 7
  6. 6. b = −10

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