Differentiating Exponential Functions

The video tutorial explains how to differentiate base B exponents by converting them into base e exponents using logarithms. It introduces the concept of using the chain rule for differentiation and provides examples to demonstrate the process. The key takeaway is that the derivative of B to the x is B to the x times the natural log of B.

What is the key concept used to differentiate base B exponents?

• Using integration by parts

• Using the quotient rule

• Using the natural base exponential function

• Using the power rule

How can a base B exponent be rewritten for differentiation?

• As a base 10 exponent

• As a base e exponent

• As a base 2 exponent

• As a base 5 exponent

What property of logarithms is used to rewrite B to the X?

• Logarithm of a product

• Logarithm of a quotient

• Exponent can come out in front

• Logarithm of a power

What rule is applied to differentiate the rewritten exponential function?

• Chain rule

• Power rule

• Quotient rule

• Product rule

What is the derivative of e to the power of a function?

• e to the power of the function times the derivative of the function

• e to the power of the function divided by the derivative of the function

• e to the power of the function plus the derivative of the function

• e to the power of the function minus the derivative of the function

What is the simplified form of the derivative of B to the X?

• B to the X times the natural log of B

• B to the X minus the natural log of B

• B to the X divided by the natural log of B

• B to the X plus the natural log of B

What is the derivative of 10 to the X?

• 10 to the X divided by the natural log of 10

• 10 to the X minus the natural log of 10

• 10 to the X plus the natural log of 10

• 10 to the X times the natural log of 10

What is the derivative of 2.3 to the X?

• 2.3 to the X minus the natural log of 2.3

• 2.3 to the X plus the natural log of 2.3

• 2.3 to the X divided by the natural log of 2.3

• 2.3 to the X times the natural log of 2.3

What additional rule is needed to differentiate 5 to the power of X squared?

• Power rule

• Product rule

• Chain rule

• Quotient rule

What is the derivative of 5 to the power of X squared?

• 5 to the power of X squared minus the natural log of 5 times 2X

• 5 to the power of X squared plus the natural log of 5 times 2X

• 5 to the power of X squared divided by the natural log of 5 times 2X

• 5 to the power of X squared times the natural log of 5 times 2X