Understanding Derivatives

This video tutorial covers various methods for finding derivatives, including the power rule, product and quotient rules, chain rule, and implicit differentiation. It explains how to differentiate constants, polynomials, rational and radical functions, trigonometric functions, logarithmic functions, and exponential functions. The video also introduces logarithmic differentiation for complex functions.

What is the derivative of a constant, such as 7?

• Undefined

• 0

• 1

• 7

Using the power rule, what is the derivative of x^3?

• x^3

• 3x

• x^2

• 3x^2

How do you find the derivative of a rational function like 1/x^2?

• Use the quotient rule directly

• Rewrite as x^-2 and apply the power rule

• Differentiate the numerator and denominator separately

• Rewrite as x^2 and apply the power rule

What is the derivative of the square root of x?

• 1/√x

• 2√x

• √x/2

• 1/(2√x)

What is the derivative of ln(x^3)?

• 1/x^3

• 3x^2

• x^2

• 3/x

What is the derivative of e raised to the power of 2x?

• e^(2x)

• 2e^x

• e^x

• 2e^(2x)

When applying the product rule, what is the derivative of x^3 multiplied by sin(x)?

• 3x^2 * sin(x) + x^3 * cos(x)

• x^3 * cos(x) + 3x^2 * sin(x)

• x^3 * sin(x) + 3x^2 * cos(x)

• 3x^2 * cos(x) + x^3 * sin(x)

Using the quotient rule, what is the derivative of (3x - 5) / (7x + 4)?

• (21x - 35) / (7x + 4)^2

• (21x + 12) / (7x + 4)^2

• (21x + 35) / (7x + 4)^2

• (47) / (7x + 4)^2

How do you find the derivative of a composite function using the chain rule?

• Subtract the derivative of the inner function from the outer function

• Differentiate the inner function and multiply by the derivative of the outer function

• Differentiate the outer function and multiply by the derivative of the inner function

• Add the derivatives of the inner and outer functions

In implicit differentiation, what must you remember to do when differentiating y with respect to x?

• Add dx/dy

• Multiply by x

• Multiply by y

• Add dy/dx