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: