1.

the derivative of `sin(log x)` is

Answer» Let `y= "sin" (log x)`
`implies(dy)/(dx)=(d)/(dx)"sin"("log"x)`
`=(1)/("log"x)(d)/(dx)("log"x)`
`=cos(log x)(d)/(dx)log x=("cos"(log x))/(x)`
`implies(d^(2)y)/(dx^(2))=(d)/(dx)[("cos"(log x))/(x)]`
`=(x(d)/(dx)"cos"(log x)-"cos"(log x)(d)/(dx)x)/(x^(2))`
`=(x{-"sin"(log x)}*(1)/(x)-"cos"(log x))/(x^(2))`
`= -[("sin"(log x) +cos(log x))/(x^(2))]`


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