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Derivatives of Inverse Trigonometric Functions
  Derivatives of Inverse Trigonometric Functions

Derivatives of Inverse Trigonometric Functions

Inverse trigonometric functions are often found in real life applications.

Derivatives of Inverse Trigonometric Functions

  1. Derivative of Inverse Sine Function

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    y is the angle lying between -π/2 and π/2 and x is the value of sine y from -1 to 1. The slope of the curve is always positive, imply dy/dx is alway positive.

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    Proof:

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  2. Derivative of Inverse Cosine Function

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    y is the angle lying between 0 and π and x is the value of cosine y from -1 to 1. The slope of the curve is always negative, imply dy/dx is alway negative.:

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    Proof:

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  3. Derivative of Inverse Tangent Function

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    y is the angle lying between -π and π and x is the value of tangent y from -∞ to +∞. The slope of the curve is always positive, imply dy/dx is alway positive.

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    Proof:

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  4. Derivative of Inverse Cotangent Function

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     y is the angle lying between 0 and π and x is the value of cotangent y from -∞ to +∞. The slope of the curve is always negative, imply dy/dx is alway negative.:

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    Or y is the angle lying between -π/2 and π/2 and x is the value of cotangent y from -∞ to +∞ and not equal to 0. The slope of the curve is always negative, imply dy/dx is alway negative.:

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    Proof:

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  5. Derivative of Inverse Secant Function

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    y is the angle lying between 0 and π and x is the value of tangent y from -∞ to -1 and from 1 to +∞. The slope of the curve is always positive, imply dy/dx is alway positive.

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    Proof:

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  6. Derivative of Inverse Cosecant Function

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    y is the angle lying between -π/2 and π/2 and x is the value of tangent y from -∞ to -1 and from 1 to +∞. The slope of the curve is always negative, imply dy/dx is alway negative.

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    Proof:

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References

  1. S. James, 1999, Calculus, Brooks/Cole Publishing Co., USA
  2. B. Joseph, 1978, University Mathematics: A Textbook for Students of Science & Engineering, Blackie & Son Limited, HongKong
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ID: 110900008 Last Updated: 6/9/2013 Revision: 1 Ref:

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