Derivatives of Exponential and Logarithmic Functions

The video tutorial explains how to find derivatives of functions using logarithmic differentiation. It provides a formula for derivatives of the form U^V and demonstrates its application through various examples, including x^x, x^sin(x), ln(x)^x, x^ln(x), x^e^x, and sin(x)^x. The video also mentions additional resources and formula sheets available in the description.

What is the first step in finding the derivative of x raised to the x using logarithmic differentiation?

• Apply the power rule

• Use the product rule

• Use logarithmic differentiation

• Differentiate directly

In the formula for the derivative of u raised to the v, what does 'v u prime' represent?

• The quotient of v and u

• The product of v and the derivative of u

• The derivative of v with respect to u

• The sum of v and u

When finding the derivative of x raised to the sin x, what is the derivative of sin x?

• 1

• x

• sin x

• cos x

What is the simplified form of the derivative of ln x raised to the x?

• x times ln x

• x raised to ln x times ln x

• ln x raised to x times 1/ln x plus ln ln x

• ln x times x

In the derivative of x raised to ln x, what is the expression for v prime?

• 1

• x

• ln x

• 1/x

What is the final simplified form of the derivative of x raised to ln x?

• x raised to ln x times ln x

• x raised to ln x times 2 ln x over x

• ln x times x

• x times ln x

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

• e^x

• 1

• x

• ln x

In the derivative of x raised to e^x, what common factor can be factored out?

• ln x

• 1/x

• x

• e^x

What is the derivative of sin x with respect to x?

• x

• 1

• sin x

• cos x

What is the final expression for the derivative of sin x raised to the x?

• sin x raised to x times x cot x plus ln sin x

• x raised to sin x times ln x

• sin x times x

• x times ln sin x