CalculusCourse skill

Differentiating sine

Differentiate sine 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 . An added constant has derivative .

Example 1

Differentiate with respect to . Angles are in radians.

Differentiate the inner expression.Sine differentiates to cosine. Multiply by the constant and the inner derivative.

Example 2

Differentiate with respect to . Angles are in radians.

Differentiate the inner expression.Sine differentiates to cosine. 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.Sine differentiates to cosine. Multiply by the constant and the inner derivative.
Question 2

Differentiate with respect to . Angles are in radians.

Check answer
Differentiate the inner expression.Sine differentiates to cosine. Multiply by the constant and the inner derivative.
Question 3

Differentiate with respect to . Angles are in radians.

Check answer
Differentiate the inner expression.Sine differentiates to cosine. Multiply by the constant and the inner derivative.
Question 4

Differentiate with respect to . Angles are in radians.

Check answer
Differentiate the inner expression.Sine differentiates to cosine. Multiply by the constant and the inner derivative.
Question 5

Differentiate with respect to . Angles are in radians.

Check answer
Differentiate the inner expression.Sine differentiates to cosine. Multiply by the constant and the inner derivative.
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