Question

Find the derivative of
$e ^{ log( {5}^{x} \times {6}^{x} )$
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Answer 1

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$\oplus\displaystyle\bf{Find \: the \: derivative \: of \: e^(log5^x\times6^x)}$

$\\ \\ \\\leadsto\displaystyle\tt{f(x)=\: e^(log5^x\times6^x)}$

$\\ \\ \\ \bullet \displaystyle\bf{By\: getting \: log \: with \: base \:e}$

$\\ \\ \\ \mapsto\displaystyle\tt{log_e f(x)=log_e e^(log5^x \times 6^x)}$

$\\ \\ \\ \mapsto\displaystyle\tt{log_e f(x)= log_e e^(logx^5+logx^6)}$

$\\ \\ \\ \mapsto\displaystyle\tt{log_e f(x)=(log_e e^logx^5+log_e e^logx^6)}$

$\\ \\ \\ \mapsto\displaystyle\tt{log_ef(x)=x^5+x^6}$

$\\ \implies\sf{\dfrac{1}{f(x) }f(x)=5x^4+6x^5}$

f(x)`=y

$\\ \implies\sf{y*=f(x)5x^4+6x^5}$

$\\\implies\sf{y*=e^(logx^5\times x^6)x^4(5+6x)}$