Math, asked by sohanreddyboppidi, 8 months ago

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

Answers

Answered by BendingReality
174

Answer:

( cos ( ㏒ x ) ) / ( x . sin ( ㏒ x ) )

Step-by-step explanation:

Let :

y = ㏒ ( sin ( ㏒ x ) )   ,   x > 0

# ㏒ x = ㏒_e x = ㏑ x

We know :

= > ( ㏑ x )' = 1 / x

= > y' = 1 / sin ( ㏒ x ) . ( sin ( ㏒ x ) )'

= >  y' = 1 / sin ( ㏒ x ) . ( cos ( ㏒ x ) ) . ( ㏒ x )'

= > y' = 1 / sin ( ㏒ x ) . ( cos ( ㏒ x ) ) . 1 / x

= > y'  = ( cos ( ㏒ x ) ) / ( x . sin ( ㏒ x ) )

Hence we get required answer!

Answered by Anonymous
40

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

By chain rule ,

 \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) \}}

Remmember :

 \star \sf  \:  \: \frac{d \{Sin(x) \}}{x}  = Cos(x) \\  \\  \star \:  \:  \sf</p><p> \frac{d \{Log(x) \}}{dx}  =  \frac{1}{x} </p><p>

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