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Calculus

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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

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.

Proof:

2. Derivative of Inverse Cosine Function

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.:

Proof:

3. Derivative of Inverse Tangent Function

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.

Proof:

4. Derivative of Inverse Cotangent Function

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.:

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.:

Proof:

5. Derivative of Inverse Secant Function

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.

Proof:

6. Derivative of Inverse Cosecant Function

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.

Proof:

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

ID: 110900008 Last Updated: 6/9/2013 Revision: 1 Ref:

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