Question

Differentoate with respect to x​

Answer 1

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Appropriate Question :

Differentiate $[\sf log \{log(logx) \}] {}^{2}$w.r.t x

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Let :

$\bf y = [log \{log(logx) \}] {}^{2}$

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To Calculate :

$\bf \large \red{dy/dx}$

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Formulae Used :

$\bigstar \: \bf \frac{d}{dx} f(x) {}^{2} = 2f(x) \frac{d}{dx} f(x) \\ \\ \bigstar \bf\frac{d}{dx} log(f(x)) = \frac{1}{f(x)} . \frac{d}{dx} f(x)$

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Solution :

$\bf y = [log \{log(logx) \}] {}^{2}$

Differentiating both side w.r.t x

$\bf\frac{dy}{dx} = \frac{d}{dx} [log \{log(logx) \}] {}^{2} \\ \\ = \sf2[log \{log(logx) \}] .\frac{d}{dx} [log \{log(logx) \}] \\ \\ = \sf 2[log \{log(logx) \}] \times \frac{1}{ \{log(log \: x) \} } \\ \times \sf\frac{ d}{dx} \{log{(log \: x)} \} \\ \\ = \sf 2[log \{log(logx) \}] \times \frac{1}{ \{log(log \: x) \} } \\ \times \sf\frac{1}{log \: x} \times \frac{d}{dx}log \: x \\ \\ = \sf 2[log \{log(logx) \}] \times \frac{1}{ \{log(log \: x) \} } \\ \times \sf\frac{1}{log \: x} \times \frac{1}{x}\\\\ \bf \frac{dy}{dx}=\frac{2[log \{log(logx) \}]}{x log \: x.\{log(log \: x) \}}$

$\large\mathfrak{ \text{W}hich \: \: is \: \: the \: \: required \: \: \text{ A}nswer.}$

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