CalculusCourse skill

Differentiating cosine

Differentiate cosine functions, including constant multiples and linear angles.

  • With angles in radians, .
  • A constant multiplier stays in front: .
  • For a linear angle, .
  • Keep the inner angle and multiply by its derivative . Remember the minus sign.

Example 1

Differentiate with respect to . Angles are in radians.

Differentiate the inner expression.Cosine differentiates to negative sine. Multiply by the constant and the inner derivative.

Example 2

Differentiate with respect to . Angles are in radians.

Differentiate the inner expression.Cosine differentiates to negative sine. Multiply by the constant and the inner derivative.

Remember
Check the inner derivative before simplifying your answer.

Your turn

Question 1

Differentiate with respect to . Angles are in radians.

Check answer
Differentiate the inner expression.Cosine differentiates to negative sine. Multiply by the constant and the inner derivative.
Question 2

Differentiate with respect to . Angles are in radians.

Check answer
Differentiate the inner expression.Cosine differentiates to negative sine. Multiply by the constant and the inner derivative.
Question 3

Differentiate with respect to . Angles are in radians.

Check answer
Differentiate the inner expression.Cosine differentiates to negative sine. Multiply by the constant and the inner derivative.
Question 4

Differentiate with respect to . Angles are in radians.

Check answer
Differentiate the inner expression.Cosine differentiates to negative sine. Multiply by the constant and the inner derivative.
Question 5

Differentiate with respect to . Angles are in radians.

Check answer
Differentiate the inner expression.Cosine differentiates to negative sine. Multiply by the constant and the inner derivative.
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