Take the derivative using chain rule of trig function and natural logarithm

The video tutorial explains how to take the derivative of the natural logarithm of a function using implicit differentiation. It starts by defining the function U as cosine of X and proceeds to find the derivative using implicit differentiation. The tutorial then simplifies the derivative to a more recognizable form, negative tangent, which is often the expected answer in multiple-choice tests.

What is the derivative of U with respect to X if U equals cosine of X?

• Sine of X

• Negative sine of X

• Cosine of X

• Negative cosine of X

In implicit differentiation, what is the derivative of Ln(U) with respect to X?

• 1/U times dU/dX

• dU/dX

• 1/U

• U times dU/dX

What is the value of U in the context of this problem?

• Cosine of X

• Tangent of X

• Sine of X

• Secant of X

How is the expression D over DX simplified in the context of this problem?

• Negative sine of X over cosine of X

• Negative cosine of X over sine of X

• Sine of X over cosine of X

• Cosine of X over sine of X

What is the simplified form of the derivative in a multiple-choice test?

• Cotangent

• Negative cotangent

• Negative tangent

• Tangent