How to take the derivative of logarithm base 4

The video tutorial covers the process of recognizing logarithms and finding derivatives, specifically focusing on the derivative of the inside function and the cosine function. The instructor explains the steps to simplify expressions and addresses errors and student confusion throughout the lesson. The tutorial emphasizes understanding the derivative process and correcting mistakes in mathematical expressions.

What is the derivative of cosine of X?

• Sine of X

• Cosine of X

• Negative sine of X

• Negative cosine of X

In the context of derivatives, what does U prime represent?

• The integral of the function

• The original function

• The second derivative of the function

• The derivative of the inside function

What was the error in the formula that needed correction?

• The use of sine instead of cosine

• The use of a negative sign instead of a positive sign

• The use of natural logarithm instead of common logarithm

• The use of cosine instead of sine

What is the simplified form of the expression involving cosine of X and 3 minus cosine of X?

• Sine of X divided by 3 minus cosine of X

• Cosine of X divided by 3 minus cosine of X

• Cosine of X divided by 3

• Sine of X divided by 3

What was the final clarification made in the session?

• The derivative of cosine is negative sine

• The derivative of sine is negative cosine

• The derivative of sine is cosine

• The derivative of cosine is positive sine