My Math Forum Derivative Problem

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 September 25th, 2011, 06:36 PM #1 Newbie   Joined: Sep 2011 Posts: 5 Thanks: 0 Derivative Problem Finding derivative of y= 2/(e^x+e^-x) and y=e^x(sinx+cosx)
 September 25th, 2011, 06:55 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs Re: Derivative Problem 1.) $y=\frac{2}{e^x+e^{-x}}=2$$e^x+e^{-x}$$^{\small{-1}}$ $\frac{dy}{dx}=-2$$e^x+e^{-x}$$^{\small{-2}}$$e^x-e^{-x}$$=\frac{-2$$e^x-e^{-x}$$}{$$e^x+e^{-x}$$^2}$ One could also write: $y=\text{sech}(x)$ $\frac{dy}{dx}=-\tanh(x)\text{sech}(x)=-$$\frac{e^x-e^{-x}}{e^x+e^{-x}}$$$$\frac{2}{e^x+e^{-x}}$$=\frac{-2$$e^x-e^{-x}$$}{$$e^x+e^{-x}$$^2}$ 2.) $y=e^x$$\sin(x)+\cos(x)$$$ $\frac{dy}{dx}=e^x$$\cos(x)-\sin(x)$$+e^x$$\sin(x)+\cos(x)$$=2e^x\cos(x)$

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