Derivatives of Inverse Trigonometric Functions

This video tutorial covers the derivatives of inverse trigonometric functions, including arc sine, arc cosine, arc tangent, arc secant, and their derivations. It provides step-by-step examples to illustrate the application of differentiation rules, implicit differentiation, and simplification techniques. The tutorial also explains the use of the chain rule and the Pythagorean theorem in deriving these derivatives.

What is the relationship between the derivatives of arc sine and arc cosine?

• They are identical.

• They are negatives of each other.

• They are reciprocals.

• They are unrelated.

Which theorem is used to find the length of the side in the derivation of the inverse sine function?

• Binomial Theorem

• Pythagorean Theorem

• Fundamental Theorem of Calculus

• Mean Value Theorem

What is the derivative of arc tangent of square root x simplified to?

• 1 divided by square root of x times (1 + x)

• 1 divided by 2 times (1 + x)

• 1 divided by square root of x

• 1 divided by 2 square root of x times (1 + x)

What is the derivative of arc tangent of square root x?

• 1 divided by square root of x

• 1 divided by 2 square root of x times (1 + x)

• 1 divided by square root of x times (1 + x)

• 1 divided by 2 times (1 + x)

In the derivative of arc secant of five x, what happens to the factor of five inside the absolute value?

• It is ignored.

• It is simplified with another factor of five.

• It is multiplied by x.

• It is squared.

What is the simplified form of the derivative of arc cosine of x over three?

• 1 divided by square root of one minus x squared

• 1 divided by square root of nine minus x squared

• Negative 1 divided by square root of one minus x squared

• Negative 1 divided by square root of nine minus x squared

What is the derivative of arc secant five x simplified to?

• 1 divided by square root of x times square root of 25x squared minus one

• 1 divided by square root of x times square root of 25x squared plus one

• 1 divided by square root of x times square root of 5x squared minus one

• 1 divided by square root of x times square root of 5x squared plus one

What is the function f(t) simplified to before finding its derivative?

• One minus t squared

• Square root of one plus t squared

• One plus t squared

• Square root of one minus t squared

Which rule is applied to find the derivative of the function involving sine and arc cosine?

• L'Hôpital's Rule

• Power Rule with Chain Rule

• Quotient Rule

• Product Rule

What is the final form of the derivative of the function involving sine and arc cosine?

• Negative t divided by square root of one minus t squared

• t divided by square root of one minus t squared

• Negative t divided by square root of one plus t squared

• t divided by square root of one plus t squared