Question

log(log x), x>1 dy/dx ज्ञात कीजिए

Answer 1

Question :-

$\to \sf log \{ log(x) \} \: \: ,x > 1 \: \: find \: \frac{dy}{dx}$

Answer :-

$\to \boxed{\sf \frac{dy}{dx} = \frac{1}{x log(x) } }$

Solution :-

$\sf let \: \: y = log \{log(x) \} \\ \\ \sf \red{mdifferentiate \: with \: respect \: to \: x} \\ \\ \to \sf \frac{dy}{dx} = \frac{d}{dx} log \{log(x) \} \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \because \sf \frac{d}{dx} log(x) = \frac{1}{x} } \\ \therefore \: \\ \to \sf \frac{dy}{dx} = \frac{1}{ log(x) } \frac{d}{dx} log(x) \\ \: \\ \to \sf \frac{dy}{dx} = \frac{1}{ log(x) } \times \frac{1}{x} \\ \\ \to \boxed{\sf \frac{dy}{dx} = \frac{1}{x log(x) } } \\ \\ \boxed{ \sf \underline{learn \: more \: question}} \\ \\ (1) \: \sf if \: y = {e}^{ \sqrt{x} } \: then \: find \: \frac{dy}{dx} \\ (2) \sf if \: y = {x}^{ \log x} \: then \: find \: \frac{dy}{dx} \\ (3) \sf if \: y = \sin \{ \cos \{sin x\} \} \: then \: find \: \frac{dy}{dx}$

Answer 2

dy/dx  = 1/xlog( x)    यदि y  = log ( log x)

Step-by-step explanation:

dy/dx ज्ञात कीजिए

y  = log ( log x)

dy/dx  = ( 1/log ( x)  )  ( d ( log x) / dx )

=> dy/dx  = ( 1/log ( x)  ) (1/x)

=> dy/dx  = 1/xlog( x)

और अधिक जानें :

sin(x²+5)"

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sin (ax+b) फलन का अवकलन कीजिए

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