Derivatives of Inverse Functions

The video tutorial covers the derivatives of inverse trigonometric functions, providing key formulas for sine inverse, cosine inverse, and tangent inverse. It includes examples demonstrating how to find derivatives of expressions like sine inverse of 2x and tan inverse of log x, using the chain rule and logarithmic differentiation. A complex example involving a linear combination of trigonometric functions within an inverse function is also solved, illustrating the application of trigonometric identities and differentiation techniques.

What is the derivative of sine inverse X?

• -1 upon root of 1 minus X square

• 1 upon 1 plus X square

• 1 upon root of 1 minus X square

• 1 upon X

Which of the following is the derivative of cos inverse X?

• -1 upon 1 plus X square

• 1 upon 1 plus X square

• -1 upon root of 1 minus X square

• 1 upon root of 1 minus X square

What is the derivative of tan inverse X?

• -1 upon root of 1 minus X square

• 1 upon 1 plus X square

• 1 upon root of 1 minus X square

• -1 upon 1 plus X square

In the example of finding the derivative of sine inverse of 2X, what additional step is required due to the chain rule?

• Divide by the derivative of 2X

• Multiply by the derivative of 2X

• Add the derivative of 2X

• Subtract the derivative of 2X

What is the derivative of sine inverse of 2X?

• 1 upon root of 1 minus 4X squared

• 2 upon root of 1 minus X squared

• 2 upon root of 1 minus 4X squared

• 1 upon root of 1 minus X squared

In the example of tan inverse of log X, what is the derivative of log X?

• 1 plus X

• log X

• X

• 1 by X

What is the derivative of tan inverse of log X?

• 1 upon X into 1 plus log X the whole square

• 1 upon X

• 1 upon 1 plus log X the whole square

• 1 upon log X

When solving problems with linear combinations inside inverse functions, what is the first step?

• Multiply the numerator by 2

• Subtract the terms in the denominator

• Add the terms in the numerator

• Split the denominator into two parts

In the example problem, what is the result of squaring and adding the constants 2 by root 13 and 3 by root 13?

• 3

• 0

• 1

• 2

What trigonometric identity is used to solve the example problem with linear combinations?

• 1 plus cot square theta equals cosec square theta

• tan square theta plus 1 equals sec square theta

• sine square theta plus cos square theta equals 1

• sine theta equals cos theta