Question

fthe deravation of (sin(logx)(x>0)

Answer 1

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

By chain rule ,

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

Remmember :

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

Answer 2

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H2O ratio by mass of combining elements 2 : 16 —>1 : 8 (H : O)

C02 ratio by mass of combining elements 12 : 32—> 3 : 08 (C : O)

NH3 ratio by mass of combining elements 14 : 3—>14 : 3 (N : H)