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Question Number 83156 by 09658867628 last updated on 28/Feb/20

$$findthederivtiveofy=e^{\cos x}$$

Commented by niroj last updated on 28/Feb/20

$$\mathrm{y}={\mathrm{e}}^{\cos \mathrm{x}}$$$$\mathrm{D}.\mathrm{w}.\mathrm{r}.\mathrm{to}\mathrm{x}.$$$$\frac{\mathrm{dy}}{\mathrm{dx}}={\mathrm{e}}^{\cos \mathrm{x}}(-\sin \mathrm{x})$$$$\frac{\mathrm{dy}}{\mathrm{dx}}=-\sin \mathrm{x}.{\mathrm{e}}^{\cos \mathrm{x}}$$

Commented by peter frank last updated on 28/Feb/20

$$lny={lne}^{\cos x}$$$$lny=\cos xlne$$$$lny=\cos x$$$$\frac{y^{{}^{\prime }}}{y}=\sin x$$$$y^{{}^{\prime }}=y\sin x$$$$y^{{}^{\prime }}=-e^{\cos x}\sin x$$

Answered by jagoll last updated on 28/Feb/20

$$\mathrm{y}{}^{\prime }=-\sin \left(\mathrm{x}\right){\mathrm{e}}^{\cos \left(\mathrm{x}\right)}$$

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