Calculus Quiz

What is the first derivative of the function f(x) =

• 
• 
• 4x^2 + 3

• 12x^2 + 6x + 2

What is the second derivative of the function f(x) = 6x^3 + 12x^2 + 5x + 2?

• 12x + 5

• 24x + 6

• 18x^2 + 24x + 5

• 36

According to the text, what is the rule for finding the nth derivative?

• f'(x) = d^2f(x)/dx^2

• f'(x) = d^f(x)/dx

• f''(x) = d^2f(x)/dx^2

• f^n(x) = d^nf(x)/dx^n

What is the implicit function given in the example?

• x^2 + y^2 = 1

• y = 4x^3 + 3x^2

• y = f(x)

• x^3y^2 + x^2 + y = 10

What is the formula for the tangent line at a point (x0, y0)?

• y = mx + b

• y = f(x0) + m(x - x0)

• y - y0 = m(x - x0)

• y - y0 = -1/m(x - x0)

What is the derivative of sin(x)?

• sin(x)

• cos(x)

• -sin(x)

• tan(x)

What is the derivative of cos(x)?

• -sin(x)

• -cos(x)

• sin(x)

• tan(x)

What is the relationship between the sine and cosine functions as stated in the text?

• sin^2(x) + cos^2(x) = 1

• sin(x) + cos(x) = 1

• sin(x) * cos(x) = 1

• sin(x) - cos(x) = 0

What is the chain rule formula as described in the text?

• dy/dx = dy/du * du/dx

• dy/dx = du/dx + dy/du

• dy/dx = du/dx * dy/du

• dy/dx = dy/dx * du/du

What is the derivative of y = x^3 + x^10?

• 3x^2 + 10x^9

• 3x^2 + 10x^10

• 3x^3 + 10x^10

• x^2 + 10x^9