Calculating Derivatives of Functions

This lesson reviews derivative formulas, including those for exponential and logarithmic functions. It provides examples of finding derivatives for various functions, such as f(x), g(x), h(x), and j(x), using different rules like the power rule and logarithmic differentiation. The video emphasizes rewriting expressions to apply these rules effectively.

What is the derivative of e^x with respect to x?

• e^x

• x^e

• ln(x)

• 1/x

How do you express the derivative of a^x with respect to x?

• x^a

• 1/a^x

• a^x

• ln(a) * a^x

What is the derivative of f(x) = 4ln(x) - 2e^x + 5x?

• 4/x + 2e^x - 5

• 4ln(x) + 2e^x - 5

• 4ln(x) - 2e^x + 5

• 4/x - 2e^x + 5

What is the derivative of g(x) = 2^x - 7x^3 + 3?

• ln(2) * 2^x - 21x^2

• 2^x + 21x^2

• ln(2) * 2^x + 21x^2

• 2^x - 21x^2

How do you express the derivative of log base b of x?

• ln(b) * x

• b^x

• 1/(ln(b) * x)

• 1/x

What is the derivative of h(x) = 9log_8(x) + 1/(6x^3)?

• 9/(ln(8) * x) - 1/(2x^4)

• 9/(ln(8) * x) + 1/(2x^4)

• 9ln(8) * x + 1/(2x^4)

• 9ln(8) * x - 1/(2x^4)

What is the derivative of j(x) = 2log(x) + 3√x?

• 2/(ln(10) * x) + 3/(2√x)

• 2ln(10) * x - 3/(2√x)

• 2ln(10) * x + 3/(2√x)

• 2/(ln(10) * x) - 3/(2√x)

How can the square root of x be expressed using exponents?

• x^1

• x^2

• x^(1/2)

• x^(1/3)

What is the derivative of a constant?

• The constant itself

• Zero

• One

• Undefined

What is the derivative of ln(x) with respect to x?

• ln(x)

• 1/x

• x

• e^x