Calculus Derivatives and Logarithms

The video tutorial covers the derivatives of exponential and logarithmic functions, starting with the basics of e^x and moving to more complex cases involving different bases. It explains the use of the chain rule, implicit differentiation, and solving equations with exponentials. The tutorial also demonstrates how to handle logarithms with bases other than e, using the change of base formula and calculator functions.

What is the derivative of e^x?

• e^2

• e^x

• x^e

• x^2

When using the chain rule for e^(3x^2 - 4x), what is the derivative of the exponent?

• 2x - 4

• 3x - 2

• 3x^2 - 4x

• 6x - 4

How can you express a^x in terms of e?

• e^(x * ln(a))

• a^(e * x)

• x^(a * e)

• e^(a * x)

What is the derivative of 2^t?

• 2^t * t

• t^2 * ln(2)

• t^2 * 2

• 2^t * ln(2)

To solve for t in 2^t = 10, which logarithm should you use?

• natural log

• log base 10

• log base e

• log base 2

What is the derivative of ln(x)?

• x

• x^2

• 1/x

• ln(x)

In the derivative of ln(x^2 + 4), what is the derivative of the internal function x^2 + 4?

• x + 4

• x^2

• 4x

• 2x

What is the change of base formula for log base a of x?

• ln(x) / ln(a)

• x / a

• a / x

• ln(a) / ln(x)

What is the derivative of log base 3 of (x^2 - 3x + 2)?

• x^2 - 3x + 2

• ln(x^2 - 3x + 2)

• ln(3)/(x^2 - 3x + 2)

• 1/(x^2 - 3x + 2) * ln(3)

Which rule is used to derive log base a of a function?

• Difference rule

• Sum rule

• Quotient rule

• Product rule