Power Rule and Derivatives

The video tutorial explains the power rule for derivatives, starting with basic examples and progressing to more complex problems involving fractions and radicals. It covers the application of the power rule to various functions, including those with negative and fractional exponents. The tutorial concludes with a summary and additional practice problems for viewers.

What does the power rule state about the derivative of x^n?

• The derivative is n times x^n

• The derivative is n times x^(n+1)

• The derivative is x^n

• The derivative is n times x^(n-1)

If f(x) = x^2, what is the derivative f'(x) using the power rule?

• 2x

• x^2

• 2x^2

• x

How do you find the derivative of a constant using the power rule?

• The derivative is the constant itself

• The derivative is the constant times x

• The derivative is one

• The derivative is zero

What is the derivative of x^(-1) using the power rule?

• x^(-2)

• -x

• 1/x

• -1/x^2

How do you apply the power rule to x^(1/2)?

• x^(-1/2)

• 1/2 * x^(-1/2)

• x^(1/2)

• 1/2 * x^(1/2)

If h(x) = x^(7/8), what is h'(x) using the power rule?

• 7/8 * x^(9/8)

• 7/8 * x^(7/8)

• 7/8 * x^(-1/8)

• 7/8 * x^(1/8)

How do you rewrite 1 over the square root of x using exponents?

• x^(1/2)

• x^(-1/2)

• x^(2)

• x^(-2)

What is the derivative of 4x^2 divided by the square root of x^10?

• -12/x^4

• 12/x^4

• -12x^4

• 12x^4

What is the derivative of e times the square root of 1 over the cube root of x?

• e/(6x^(1/6))

• -e/(6x^(7/6))

• e/(6x^(7/6))

• -e/(6x^(1/6))

What is the derivative of 4x^π using the power rule?

• 4πx^(π-1)

• 4πx^π

• 4x^(π-1)

• πx^(π-1)