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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 ?...
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 Spring '08
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 Calculus, Derivative, Power Rule

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