Math, asked by wwwvinodalax2617, 1 year ago

e^3logx differentiate it

Answers

Answered by dhruvsh
11

Answer:

e^3log x = e^log x^3 = x^3

So,

d(x^3)/dx = 3x^2

Answered by shadowsabers03
13

We have to find,

\dfrac{d}{dx}\ e^{^{\displaystyle\small\text{$3\log(x)$}}}

First let me convert the common logarithm to natural logarithm. We know it.

\log(x)=\dfrac{\ln(x)}{\ln(10)}\ \ \ \left[\because\ \log_b(a)\ =\ \dfrac{\log_m(a)}{\log_m(b)}\right]

So,

\dfrac{d}{dx}\ e^{^{\displaystyle\small\text{$3\log(x)$}}}\ \implies\ \dfrac{d}{dx}\ e^{\displaystyle\small\text{$\dfrac{3\ln(x)}{\ln(10)}$}}

And we have the exponential function rule of differentiation.

\dfrac{d}{dx}\ e^{f(x)}\ =\ e^{f(x)}\ \cdot\ \dfrac{d(f(x))}{dx}

So,

\dfrac{d}{dx}\ e^{\displaystyle\small\text{$\dfrac{3\ln(x)}{\ln(10)}$}}\ \implies\ e^{\displaystyle\small\text{$\dfrac{3\ln(x)}{\ln(10)}$}}\ \cdot\ \dfrac{d}{dx}\left(\dfrac{3\ln(x)}{\ln(10)}\right)\\ \\ \\ \implies\ e^{\displaystyle\small\text{$\dfrac{3\ln(x)}{\ln(10)}$}}\ \cdot\ \dfrac{3}{\ln(10)}\ \cdot\ \dfrac{d}{dx}\ \ln(x)\\ \\ \\ \implies\ e^{\displaystyle\small\text{$\dfrac{3\ln(x)}{\ln(10)}$}}\ \cdot \dfrac{3}{\ln(10)}\ \cdot\ \dfrac{1}{x}

\implies\ \boxed{\dfrac{3\cdot e^{\displaystyle\small\text{$\dfrac{3\ln(x)}{\ln(10)}$}}}{x\cdot \ln(10)}}

Hence differentiated!


pratyush4211: As Always Great Answer
pratyush4211: (*❛‿❛)→
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