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Answer 1 · 2017-11-26T05:15:49

#(-9picos((9pi)/x))/x^2#

Differentiating with respect to #x#, we'll treat #pi# as a constant and apply the chain rule.

The chain states: #d/dx[f(g(x))]=f'(g(x))*g'(x)#

So...

#d/dx[sin(9pi)/x]=cos((9pi)/x)*color(red)(d/dx[(9pi)/x]#

#color(red)(d/dx[(9pi)/x]=9pi*d/dx(1/x)=9pi*d/dx(x^-1)#

Appling the power rule we get:

#9pi*-1/x^2=-(9pi)/x^2#

Therefore,

#d/dx[sin(9pi)/x]=cos((9pi)/x)*-(9pi)/x^2#

#=(-9picos((9pi)/x))/x^2#