How to Differentiate Inverse Trigonometric Functions

Derivatives of arcsin(x)

1/√(1-x²).

Derivatives of arccos(x)

-1/√(1-x²).

Derivatives of arctan(x)

1/(1+x²).

Derivatives of arccot(x)

-1/(1+x²).

Derivatives of arcsec(x)

1/(|x|√(x²-1)).

Derivatives of arccsc(x)

-1/(|x|√(x²-1)).

Angled Relationships

Inverse trigonometric functions help describe relationships between angles and triangle sides.

Differentiation Formulas

Unique formulas that specify the derivatives of each of the six inverse trigonometric functions.

Function Recognition

Identify the specific inverse trigonometric function present in a differentiation problem.

Simplifying Arguments

Reducing the complexity of a function's input before applying differentiation.

Application in Integration

Inverse trigonometric functions are often used in solving integrals involving complex expressions.

Geometric Interpretation

Understanding the derivatives of inverse trigonometric functions through geometric models and relationships.

Critical Skill in Calculus

Differentiating inverse trigonometric functions is essential for mastering calculus concepts.

Example Problems

Illustrations or practical applications that demonstrate the differentiation of inverse trigonometric functions.