QZ-Derivative of Inverse Trigonometric Functions-1

Front

What is the derivative of the inverse sine function (sin^(-1)(x))?

Back

The derivative of sin^(-1)(x) is 1/√(1-x²) for -1 < x < 1.

Front

What is the derivative of the inverse cosine function (cos^(-1)(x))?

Back

The derivative of cos^(-1)(x) is -1/√(1-x²) for -1 < x < 1.

Front

What is the derivative of the inverse tangent function (tan^(-1)(x))?

Back

The derivative of tan^(-1)(x) is 1/(1+x²) for all x.

Front

What is the derivative of the inverse cotangent function (cot^(-1)(x))?

Back

The derivative of cot^(-1)(x) is -1/(1+x²) for all x.

Front

What is the derivative of the inverse secant function (sec^(-1)(x))?

Back

The derivative of sec^(-1)(x) is 1/(|x|√(x²-1)) for |x| > 1.

Front

What is the derivative of the inverse cosecant function (csc^(-1)(x))?

Back

The derivative of csc^(-1)(x) is -1/(|x|√(x²-1)) for |x| > 1.

Front

What is the relationship between the derivatives of inverse trigonometric functions and their corresponding trigonometric functions?

Back

The derivatives of inverse trigonometric functions are the reciprocals of the derivatives of their corresponding trigonometric functions.

Front

How can you derive the formula for the derivative of sin^(-1)(x)?

Back

Using implicit differentiation: if y = sin^(-1)(x), then x = sin(y). Differentiate both sides with respect to x.

Front

What is the range of the inverse sine function?

Back

The range of sin^(-1)(x) is [-π/2, π/2].

Front

What is the range of the inverse cosine function?

Back

The range of cos^(-1)(x) is [0, π].