Question

Inverse trigonometric derivatives calculator.

A) Differentiate using standard rules.
B) The derivatives of inverse trigonometric functions cannot be calculated.
C) Use the chain rule and known derivatives of inverse trigonometric functions.
D) Inverse trigonometric derivatives are always zero.

Answer 1

The derivatives of inverse trigonometric functions can be calculated using the chain rule and known derivatives of inverse trigonometric functions.

Step-by-step explanation:

The derivatives of inverse trigonometric functions can be calculated using the chain rule and known derivatives of inverse trigonometric functions. To differentiate the inverse trigonometric functions, we use the following formulas:

• d/dx (arcsin(x)) = 1 / sqrt(1 - x^2)
• d/dx (arccos(x)) = -1 / sqrt(1 - x^2)
• d/dx (arctan(x)) = 1 / (1 + x^2)

These formulas can be derived using the basic trigonometric identities and the chain rule. For example, to differentiate the inverse sine function, we start with the derivative of sine: d/dx (sin(x)) = cos(x). Then, using the chain rule, we have d/dx (arcsin(x)) = 1 / (cos(arcsin(x))), which simplifies to 1 / sqrt(1 - x^2).