Understanding the Constant Multiple Rule for Derivatives

This video tutorial explains the constant multiple rule for derivatives, demonstrating how to differentiate functions with constant coefficients. It includes examples such as differentiating 3x^5, 4x^7, and 5x^9, and extends to fractional and rational functions. Advanced examples cover negative coefficients and square roots, culminating in a complex example involving roots and exponents.

What is the constant multiple rule for derivatives?

• The derivative of a constant times a function is the constant times the derivative of the function.

• The derivative of a function is the constant times the function.

• The derivative of a constant is the function times the constant.

• The derivative of a function is the constant divided by the function.

Using the constant multiple rule, what is the derivative of 4x^7?

• 7x^6

• 4x^6

• 28x^7

• 28x^6

How do you differentiate x divided by 7 using the constant multiple rule?

• x^7

• 7x

• x/7

• 1/7

What is the derivative of x^3 divided by 15?

• x^2/5

• 3x^3/15

• x^3/15

• 3x^2/15

What is the derivative of 4√x using the constant multiple rule?

• 4√x

• 2√x

• 4/√x

• 2/√x

How do you differentiate 5/x using the constant multiple rule?

• -5/x^2

• 5/x^2

• -5x

• 5x

What is the derivative of negative seven x^6 divided by four?

• -21x^5/2

• -42x^5/4

• -21x^6/2

• -42x^6/4

What is the derivative of 5 divided by the seventh root of x^4?

• -5/7 * x^4

• 10/7 * x * 7th root of x^4

• 5/7 * x^4

• -10/7 * x * 7th root of x^4

How can you simplify the expression -10/7 * x * 7th root of x^4?

• -10 * 7th root of x^4 / 7x

• -10 * 7th root of x^3 / 7x^2

• 10 * 7th root of x^4 / 7x

• 10 * 7th root of x^3 / 7x^2

What is the simplified form of the derivative of 5 divided by the seventh root of x^4?

• -5/7 * x^4

• -10/7 * x * 7th root of x^4

• 5/7 * x^4

• 10/7 * x * 7th root of x^4