Find the derivative of exponential with the base as a fraction

The video tutorial explains the importance of rewriting exponentials for derivative calculations. It covers the process of rewriting functions, taking derivatives, and handling negatives in the calculations. The tutorial emphasizes the need to multiply by the natural logarithm of the base and the derivative of the inside function, highlighting the importance of correctly managing negative signs to avoid errors.

What is the significance of rewriting exponentials in calculus?

Explain the process of taking the derivative of a function that involves cosine.

How does the presence of a negative sign affect the derivative of cosine?

Describe the relationship between the derivative of cosine and sine.

What would happen if the base of the exponential was not included in the derivative calculation?