MATH-M 211 Lecture Notes - Lecture 5: Differentiable Function, Rational Number, Power Rule
Document Summary
Section 2. 2 notes- basic differentiation rules and rates of change. Constant rule- derivative of constant function = 0: if c is real number, then. Constant multiple rule- if f is differentiable function and c is real number, then cf is also differentiable o. Derivatives of sine and cosine functions: sine- If f(x) = xn, use definition of derivative to find f"(x)- not needed, but for understanding why it all works . Slope- rate of change: rate of change of y with respect to x is. Slope of secant line (2 points on function: derivative. Slope of tangent line (1 point on function: velocity- distance or position in relation to time. Position function- s(t) v(t) = s"(t) = instantaneous velocity function a(t) = v"(t) = s (t) = acceleration function (second derivative of position) Velocity can be +, -, or 0. Speed = |velocity| = always positive: position of free-falling objects.
