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Question Number 102508 by Study last updated on 09/Jul/20

$$li\underset{△x\to 0}{m}\frac{e^{sin(x-△x)}-e^{sinx}}{△x}=?$$

Commented by bemath last updated on 09/Jul/20

$$maybe\underset{\mathrm{\Delta }x\to 0}{\lim }\frac{e^{\sin (x+\mathrm{\Delta }x)}-e^{\sin x}}{\mathrm{\Delta }x}$$

Commented by Study last updated on 09/Jul/20

$$nosir$$

Commented by Study last updated on 09/Jul/20

$$helpme$$

Commented by bemath last updated on 09/Jul/20

$$usingLHopital$$

Commented by Dwaipayan Shikari last updated on 09/Jul/20

$$l\underset{x\to 0}{\lim }\frac{e^{sinx}\left(e^{sin(x-△x)-sinx}\right)}{△x}=\frac{e^{sinx}\left(e^{-2cos(x-\frac{△x}{2})sin\frac{△x}{2}}\right)}{△x}=e^{sinx}.\frac{e^{-cosx△x}}{△x}$$$$e^{sinx-cosx△x}.\frac{1}{△x}=y$$$$$$$$$$$$If(e^{sin(x+△x)}-e^{sinx}).\frac{1}{△x}=cosx{e}^{sinx}$$

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