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Questions and Answers
What is the derivative of y = sin⁻¹ x?
What is the derivative of y = sin⁻¹ x?
- $ rac{1}{ an y}$
- $ rac{1}{ orall x}$
- $ rac{1}{ ext{cos} y}$ (correct)
- $ rac{1}{ ext{sec} y}$
What is the domain of the function y = sin⁻¹ x?
What is the domain of the function y = sin⁻¹ x?
- [-1, 1] (correct)
- (-1, 1)
- [-π/2, π/2]
- [0, 1]
In the context of inverse trigonometric functions, which statement is true regarding the range of y = sin⁻¹ x?
In the context of inverse trigonometric functions, which statement is true regarding the range of y = sin⁻¹ x?
- The range is [-π/2, π/2] (correct)
- The range is [-π, π]
- The range is [0, 1]
- The range is [0, π/2]
What condition is necessary for the function y = sin⁻¹ u to have a defined derivative?
What condition is necessary for the function y = sin⁻¹ u to have a defined derivative?
How is $ rac{dy}{dx}$ expressed when y = sin⁻¹ u?
How is $ rac{dy}{dx}$ expressed when y = sin⁻¹ u?
Flashcards
Derivative of sin⁻¹ x
Derivative of sin⁻¹ x
The rate of change of y = sin⁻¹ x is dy/dx = 1/√(1-x²) for x ∈ (-1, 1).
Domain of sin⁻¹ x
Domain of sin⁻¹ x
The range of x-values for y = sin⁻¹ x is [-1, 1].
Range of sin⁻¹ x
Range of sin⁻¹ x
The output values for sin⁻¹ x fall within [-π/2, π/2].
Implicit differentiation
Implicit differentiation
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General derivative formula
General derivative formula
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