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how to differentiate lnfx. Hence ddxexlnxlnx1exlnx by the chain rule and using the fact that the derivative of efxfxefx for any differentiable function fx. D dx lnfx fx fx 2x x 2 5 3The final answer is d dx lnx 2 5 2x x 2 5.
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Ln f x lnf x Since this is a composite function we can differentiate it using chain rule. Ln as inverse function of exponential function The natural logarithm function ln x is the inverse function of the exponential function e x. First let Fx ln 2 x Then remember that ln 2 x is equal to lnxlnx So Fx lnxlnx By setting fx and gx as lnx means that Fx fxgx and we can apply the product rule to find Fx remembering that the derivative of lnx is 1x.
Fgx ln2x fgx 12x The derivative of ln2x with respect to 2x is 12x 1x.
Hence ddxexlnxlnx1exlnx by the chain rule and using the fact that the derivative of efxfxefx for any differentiable function fx. Hence ddxexlnxlnx1exlnx by the chain rule and using the fact that the derivative of efxfxefx for any differentiable function fx. First let Fx ln 2 x Then remember that ln 2 x is equal to lnxlnx So Fx lnxlnx By setting fx and gx as lnx means that Fx fxgx and we can apply the product rule to find Fx remembering that the derivative of lnx is 1x. Y 2 ln 3x 2 1.
