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Differentiate the following function ...

Differentiate the following function from first principles: `e^(cosx)`

Text Solution

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We have given: `e^(cosx)`
Let `y=f(x)=e^(cosx)`br> Now differentiating w.r.to `x` by using first principle we get
`implies f(x+h)=e^(cos(x+h))`
Hence,
`d/(dx)(f(x))=lim_(h->0)(f(x+h)-f(x))/h`
`d/(dx)(f(x))=lim_(h->0)(e^(cos(x+h))-e^(cosx))/h`
`d/(dx)(f(x))=lim_(h->0) (e^(cosx)(e^(cos(x+h)-cosx))-1)/h`
...
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