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Derivatives of Trigonometric, Exponential and Logarithmic Functions (Calculus I)

Free printable university Calculus I worksheet: derivatives of sin, cos and tan, exponential functions (including general bases), and logarithms, combined with the product and chain rules. Angles in radians; every derivative cross-checked numerically.

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Calculus I · Math worksheet
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Derivatives of Trigonometric, Exponential and Logarithmic Functions

Differentiate each function. Angles are in radians. Remember: (sin u)' = cos(u)u', (cos u)' = -sin(u)u', (tan u)' = sec^2(u)u', (e^u)' = e^u u', (ln u)' = u'/u.

  1. 1.
    Differentiate f(x) = -sin(4x) + 4 cos(x).
  2. 2.
    Differentiate f(x) = 4 sin(3x) + 4 cos(2x).
  3. 3.
    Differentiate f(x) = sin(4x) + 4 cos(2x).
  4. 4.
    Differentiate f(x) = tan(x).
  5. 5.
    Differentiate f(x) = tan(3x).
  6. 6.
    Differentiate f(x) = sin(x2x^{2} + 1).
  7. 7.
    Differentiate f(x) = sin2(x).
  8. 8.
    Differentiate f(x) = -3e^(-x).
  9. 9.
    Differentiate f(x) = -4e^x.
  10. 10.
    Differentiate f(x) = ex2e^{x^{2}}.
  11. 11.
    Differentiate f(x) = 2x2^{x}.
  12. 12.
    Differentiate f(x) = ln(4x), for 4x > 0.
  13. 13.
    Differentiate f(x) = ln(4x + 2), for 4x + 2 > 0.
  14. 14.
    Differentiate f(x) = x ln(x), for x > 0.
  15. 15.
    Differentiate f(x) = x exe^{x}.
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