### Derivative of inverse trigonometric functions.

 To find the inverse functions, if y = f(x) then x = f-1(y) or if x = g(y) then y = g-1(x) or use dy/dx = 1/(dx/dy) Derivative of sin-1 x y = sin-1 x x = sin y dy/dx = 1/(dx/dy) dy/dx = 1/d(sin y)/dy = 1/cos y = 1/√(1 - x2) d(sin-1 x)/dx = 1/√(1 - x2) Derivative of cos-1 x y = cos-1 x x = cos y dy/dx = 1/(dx/dy) dy/dx = 1/d(cos y)/dy = -1/sin y = -1/√(1 - x2) d(cos-1 x)/dx = -1/√(1 - x2) Derivative of tan-1 x y = tan-1 x x = tan y dy/dx = 1/(dx/dy) dy/dx = 1/d(tan y)/dy = 1/sec2 y = cos2 y = 1/(1 + x2) d(tan-1 x)/dx = 1/(1 + x2) Derivative of cot-1 x y = cot-1 x x = cot y dy/dx = 1/(dx/dy) dy/dx = 1/d(cot y)/dy = -1/cosec2 y = -sin2 y = -1/(1 + x2) d(cot-1 x)/dx = -1/(1 + x2) Derivative of sec-1 x y = sec-1 x x = sec y dy/dx = 1/(dx/dy) dy/dx = 1/d(sec y)/dy = 1/sec y tan y = 1/x√(x2 - 1) d(sec-1 x)/dx = 1/√(x2 - 1) Derivative of cosec-1 x y = cosec-1 x x = cosec y dy/dx = 1/(dx/dy) dy/dx = 1/d(cosec y)/dy = -1/cosec y cot y = -1/x√(x2 - 1) d(cosec-1 x)/dx = -1/√(x2 - 1)