Topic 3: Slopes and Derivative

What is a derivative?

The derivative expresses the rate of change of a function with respect to an independent variable.

What does the first derivative represent?

The slope of the tangent line to the curve.

What are common symbols for derivative?

dy/dx, y′, Dxy, and f′(x).

What is differentiation?

The operation of finding the derivative.

What is the derivative definition using limits?

dy/dx = lim Δx→0 (Δy/Δx).

What is the constant rule?

d/dx(c) = 0.

What is the sum rule?

d/dx(u+v) = du/dx + dv/dx.

What is the product rule?

d/dx(uv) = u(dv/dx) + v(du/dx).

What is the quotient rule?

d/dx(u/v) = (v du/dx - u dv/dx)/v².

What is the power rule?

d/dx(uⁿ) = n uⁿ⁻¹ du/dx.

What is the derivative of eᵘ?

d/dx(eᵘ) = eᵘ du/dx.

What are higher derivatives?

Derivatives of derivatives, such as the second and third derivatives.