Derivatives of Common Functions

The video tutorial covers various differentiation techniques, including the power rule, chain rule, and differentiation of trigonometric, logarithmic, and exponential functions. It provides examples and practice problems to help understand these concepts. The tutorial emphasizes the importance of maintaining the same argument in trigonometric differentiation and explains the chain rule's application in different contexts.

What is the derivative of a constant function?

• Undefined

• The constant itself

• 1

• 0

If y = x^3, what is dy/dx?

• 3x^2

• x^3

• x^2

• 3x

If y = x^2 + 1, what is dy/dx?

• x^2

• 2x + 1

• x

• 2x

What is the derivative of x^n?

• nx^n

• x^n

• nx^(n-1)

• n^x

What is the derivative of x^3 + 3x?

• 3x^2 + 3

• 3x^2

• 3x + 3

• x^3

What is the derivative of x^4?

• 4x

• x^4

• x^3

• 4x^3

What is the derivative of x^5?

• x^4

• 5x^4

• x^5

• 5x

What is the derivative of x^6?

• 6x

• x^6

• x^5

• 6x^5

What is the derivative of x^7?

• x^6

• x^7

• 7x^6

• 7x

What is the derivative of x^8?

• 8x^7

• x^7

• 8x

• x^8