Question

differentiate y=e^secx
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ASAP ANSWER
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Answer 1

Solution :

Given, y = $\mathrm{e^{secx}}$

Differentiating both sides w.r.t. x, we get

$\mathrm{\frac{dy}{dx}=\frac{d}{dx}(e^{secx})}$

$\mathrm{=e^{secx}\frac{d}{dx}(secx)}$

$\mathrm{=e^{secx}\:secx\:tanx}$

$\to \boxed{\mathrm{\frac{dy}{dx}=e^{secx}\:secx\:tanx}}$

which is the required differentiation.

Rule :

$\mathrm{\frac{d}{dx}e^{g(x)}=e^{g(x)}\:g'(x)}$ ,

where $\mathrm{g'(x)=\frac{d}{dx}g(x)}$