Calculus Derivatives and Rules

This video tutorial covers various differentiation formulas essential for calculus, including the power rule, product and quotient rules, chain rule, and derivatives of exponential, logarithmic, trigonometric, and inverse trigonometric functions. It provides examples and explanations to help students understand and apply these concepts effectively.

What is the derivative of a constant?

• Undefined

• The constant itself

• Zero

• One

Using the power rule, what is the derivative of x^4?

• 4x^5

• 3x^4

• 4x^3

• x^3

What is the derivative of a^x, where a is a constant?

• a^x * a

• a^x * ln(a)

• x^a * ln(x)

• a^x * x

Which rule is used to find the derivative of a product of two functions?

• Chain rule

• Power rule

• Product rule

• Quotient rule

What is the formula for the quotient rule?

• u' * v - v' * u

• v * u' - u * v' / v^2

• u / v'

• u * v' + v * u'

In the chain rule, what do you differentiate first?

• The variable

• The outer function

• The inner function

• The constant

How do you find the derivative of log base a of u?

• ln(a) / u'

• u' / (u * ln(a))

• u' * ln(a)

• u / ln(a)

What is the derivative of sin(u)?

• sec(u) * u'

• -sin(u) * u'

• tan(u) * u'

• cos(u) * u'

What is the derivative of the inverse sine function?

• u' / sqrt(1 - u^2)

• -u' / sqrt(1 - u^2)

• u / sqrt(1 - u^2)

• 1 / sqrt(1 - u^2)

Which of the following is the derivative of sec(u)?

• sec(u) * tan(u) * u'

• -sec(u) * tan(u) * u'

• sec(u) * u'

• tan(u) * u'