Differentiation Techniques and Rules

This video tutorial covers the basics of finding derivatives, including the power rule, derivatives of constants, polynomials, radical and rational functions, trigonometric functions, exponential and logarithmic functions, and the product rule. It provides examples and explanations for each type of function, helping viewers understand how to apply differentiation rules effectively.

What is the derivative of x^3 using the power rule?

• 3x^2

• 2x^3

• x^2

• 3x^3

How do you find the derivative of a constant?

• Divide by the constant

• Use the power rule

• Add one to the constant

• Multiply by zero

What is the derivative of the square root of x?

• 1/√x

• 2√x

• 1/(2√x)

• √x/2

How do you handle negative exponents when differentiating?

• Add one to the exponent

• Move the variable to the denominator

• Multiply by zero

• Ignore the negative sign

What is the derivative of sin(x)?

• cos(x)

• -sin(x)

• tan(x)

• -cos(x)

Which trigonometric function's derivative is negative cosecant squared?

• cotangent

• cosine

• secant

• sine

What is the derivative of e^(7x)?

• 7e^(7x)

• e^(x)

• e^(7x)

• 7x

How do you differentiate e^(x^2)?

• 2xe^(x^2)

• e^(x^2)

• x^2e^(x^2)

• 2e^(x^2)

What is the derivative of ln(x)?

• ln(x)

• x^2

• 1/x

• x

When is the product rule used in differentiation?

• When two functions are multiplied

• When a function is subtracted

• When a function is divided

• When a function is added