This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture 11 — Derivatives of Elementary Functions Constant Function: d dx c = Power Rule: For all real n 6 = 0 , d dx x n = We can combine these results with the following one in order to take the derivative of any linear combination of functions, such as polynomials: If functions f and g are differentiable at x , then for any constants a and b , d dx h af ( x ) + bg ( x ) i = d dx h 1 + x ( x 1) 2 i = d 2 dx 2 h 1 + x ( x 1) 2 i = Where does the graph of the function P ( t ) = t 3 √ t + 1 3 √ t 2 have horizontal and vertical tangent lines? Find the rate at which the volume of a sphere changes with respect to the radius and interpret when r = . 5 inches and r = 3 inches. The frequency of vibration in Hertz of a cello string is described by f = k √ T 2 L for some constant k , where L is the length of the string in meters, T is the tension in Newtons. Find df dT and df dL and interpret. Can power rule be applied to find the derivatives of e x or x x ?...
View
Full Document
 Spring '08
 ALL
 Calculus, Derivative, Power Rule, ax, dx, vertical tangent lines

Click to edit the document details