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.

Why is it important to rewrite exponentials when taking derivatives?

• To make the expression more complex

• To avoid dealing with fractions

• To increase the number of terms

• To eliminate the need for logarithms

What is the rewritten form of the expression involving cosine?

• 4 to the power of cosine of x

• Negative 4 times cosine of x

• 4 to the power of negative cosine of x

• Cosine of x times 4

What mathematical operation is used after rewriting the exponential expression?

• Multiplication by the natural logarithm of the base

• Addition of the base

• Division by the derivative of the base

• Subtraction of the inside function

What is the derivative of cosine of x?

• Cosine of x

• Negative cosine of x

• Negative sine of x

• Sine of x

Why is it important to consider the sign when calculating the derivative?

• To make the calculation easier

• To avoid missing a sine term

• To ensure the result is always negative

• To eliminate the need for rewriting