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 is equal to cosine of X?

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Explain the process of implicit differentiation as mentioned in the text.

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What is the relationship between DUDX and the sine and cosine functions as described?

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How does the text derive the expression for D over DX in terms of sine and cosine?

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What would be the final answer on a multiple choice test based on the calculations provided?

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