Derivatives Quiz

What is the power rule for differentiation?

• f'(x) = nx^(n+1)

• f'(x) = n^(n-1)

• f'(x) = x^(n-1)

• f'(x) = nx^(n-1)

Differentiate the function f(x) = 3x^2 using the power rule.

• 6x

• 9x

• 3x^2

• 6x^2

What is the chain rule used for in calculus?

• To find the maximum or minimum value of a composite function.

• To find the limit of a composite function.

• To find the integral of a composite function.

• To find the derivative of a composite function.

Find the derivative of g(x) = (2x^3 + 5x^2)^4 using the chain rule.

• 4*(2x^3 + 5x^2)^3*(6x^2 + 10x)

• 4*(2x^3 + 5x^2)^4*(6x^2 + 10x)

• 4*(2x^3 + 5x^2)^2*(6x^2 + 10x)

• 4*(2x^3 + 5x^2)^3*(6x^2 + 10x) + 1

What is the general formula for the power rule?

• d/dx(x^n) = x^(n-1)

• d/dx(x^n) = nx^(n+1)

• d/dx(x^n) = (n-1)x^n

• d/dx(x^n) = nx^(n-1)

Differentiate the function h(x) = 4x^5 - 2x^3 + 7x - 9 using the power rule.

• 20x^4 - 6x^2 + 7x - 9

• 4x^5 - 2x^3 + 7

• 20x^4 - 6x^2 + 7

• 20x^4 - 6x^2 + 7x

What is the chain rule formula for composite functions?

• dy/dx = f'(g(x)) * g'(x)

• dy/dx = f'(g(x)) - g'(x)

• dy/dx = f'(g(x)) + g'(x)

• dy/dx = f'(g(x)) / g'(x)

Find the derivative of f(x) = sin(2x) using the chain rule.

• 2sin(2x)

• cos(2x)

• sin(2x)

• 2cos(2x)

What is the power rule for negative exponents?

• a^(-n) = -1/(a^n)

• a^(-n) = 1/(a^n)

• a^(-n) = a^n

• a^(-n) = n/(a^n)

Differentiate the function g(x) = 1/x^2 using the power rule for negative exponents.

• -2x^(-3)

• -2x^(-4)

• -2x^(-2)

• -2x^(-1)