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Question Number 167357 by mkam last updated on 13/Mar/22

$$find{n}^{th}dervaiteveofln\left(cosx\right)?$$

Answered by Coronavirus last updated on 16/Mar/22

$$$$$$posonsf\left(x\right)=ln\left(\cos \left(x\right)\right)$$$$$$$$\partial f=-\tan \left(x\right)$$$${\partial }^{2}f=-1-{\tan }^2\left(\mathrm{x}\right)$$$${\partial }^{3}f=-2\tan \left(\mathrm{x}\right)-{2\tan }^3\left(\mathrm{x}\right)$$$${\partial }^{4}f=-{4\tan }^2\left(\mathrm{x}\right)-{6\tan }^4\left(\mathrm{x}\right)+2$$$$\mathrm{et}\mathrm{omme}\tan \left(\mathrm{x}\right)=\sin \left(\mathrm{x}\right)\times \frac{1}{\cos \left(\mathrm{x}\right)}$$$$apresjepense\stackrel{`}{a}utiliserlaflormuledeLeibniz$$$${\partial }^n(f.g)=\underset{i=0}{\sum ^{\mathrm{n}}}{\mathrm{C}}_n^i\left({\partial }^i{f}^{}\right)\left({\partial }^{n-i}g\right)$$

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