Question

The derivative of log (sin(logx) (x > 0) ​khh

Answer 1

Answer:

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→ The correct answer is cotx. Differentiate equation on both sides with respect to x. The differentiation of sinx is cosx and the differentiation of logx is 1\x.

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Hope it helps you dear!

Answer 2

Let , y = Log{Sin(Log(x)}

By chain rule ,

$\begin{gathered}\sf \mapsto \frac{dy}{dx} = \frac{1}{Sin \{Log(x) \}} \times \frac{d \{Sin \{Log(x) \} \}}{dx} \\ \\ \sf \mapsto \frac{dy}{dx} =\frac{1}{Sin \{Log(x) \}} \times Cos \{Log(x) \} \times \frac{d \{Log(x) \}}{dx} \\ \\ \sf \mapsto \frac{dy}{dx} = \frac{1}{Sin \{Log(x) \}} \times Cos \{Log(x) \} \times \frac{1}{x} \\ \\ \sf \mapsto \frac{dy}{dx} = \frac{Cos \{Log(x) \}}{x.Sin \{Log(x) \}}\end{gathered}$

Remmember :

$\begin{gathered}\star \sf \: \: \frac{d \{Sin(x) \}}{x} = Cos(x) \\ \\ \star \: \: \sf \frac{d \{Log(x) \}}{dx} = \frac{1}{x}\end{gathered}$