Derivatives of Inverse Trigonometric Functions

This video tutorial covers the derivatives of inverse trigonometric functions, including inverse sine, cosine, tangent, secant, cotangent, and cosecant. Each section explains the derivative formula for a specific inverse trig function, provides examples, and demonstrates how to apply the formulas to solve problems. The video emphasizes understanding the formulas and simplifying expressions where possible.

What is the derivative of the inverse sine function in terms of u?

• u' divided by the square root of 1 plus u squared

• Negative u' divided by the square root of 1 minus u squared

• u' divided by the square root of 1 minus u squared

• u' divided by 1 plus u squared

How does the derivative of the inverse cosine function differ from that of the inverse sine?

• It is negative instead of positive

• It is multiplied by the square root of 1 minus u squared

• It is positive instead of negative

• It is divided by 1 plus u squared

What is the formula for the derivative of the inverse tangent function?

• Negative u' divided by 1 plus u squared

• u' divided by 1 plus u squared

• Negative u' divided by the square root of 1 minus u squared

• u' divided by the square root of 1 minus u squared

In the example of inverse tangent, what is the simplified form of the derivative of inverse tangent of x/2?

• 1 divided by 4 plus x squared

• 1 divided by 2 plus x squared

• 2 divided by 4 plus x squared

• 2 divided by 1 plus x squared

What is the derivative of the inverse secant function in terms of u?

• u' divided by 1 plus u squared

• Negative u' divided by the absolute value of u times the square root of u squared minus 1

• Negative u' divided by 1 plus u squared

• u' divided by the absolute value of u times the square root of u squared minus 1

In the example of inverse secant, what is the simplified form of the derivative of inverse secant of 1 + x squared?

• 2 divided by the absolute value of 1 minus x squared times the square root of x squared plus 2

• 2 divided by the absolute value of 1 plus x squared times the square root of x squared minus 2

• 2 divided by the absolute value of 1 minus x squared times the square root of x squared minus 2

• 2 divided by the absolute value of 1 plus x squared times the square root of x squared plus 2

What is the formula for the derivative of the inverse cotangent function?

• u' divided by 1 plus u squared

• Negative u' divided by 1 plus u squared

• Negative u' divided by the square root of 1 minus u squared

• u' divided by the square root of 1 minus u squared

How does the derivative of the inverse cosecant function compare to that of the inverse secant?

• It is negative instead of positive

• It is multiplied by the square root of 1 minus u squared

• It is positive instead of negative

• It is divided by 1 plus u squared

What is the derivative of the inverse cosecant function in terms of u?

• u' divided by the absolute value of u times the square root of u squared minus 1

• Negative u' divided by the absolute value of u times the square root of u squared minus 1

• u' divided by 1 plus u squared

• Negative u' divided by 1 plus u squared

In the example of inverse cotangent, what is the simplified form of the derivative of inverse cotangent of 3x?

• 3 divided by 1 plus 3x squared

• Negative 3 divided by 1 plus 3x squared

• 3 divided by 1 plus 9x squared

• Negative 3 divided by 1 plus 9x squared