What is the derivative of #f(x)=picos((x-1)/x^2)#?

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Answer 1 · 2018-05-20T10:06:19

#(π(x-2)sin((x-1)/x^2))/x^3#

#f(x)=(πcos((x-1)/x^2))'# #=#

#-πsin((x-1)/x^2)((x-1)/x^2)'=#

#-πsin((x-1)/x^2)*((x-1)'x^2-(x-1)(x^2)')/x^4=#

#-πsin((x-1)/x^2)*(x^2-(x-1)(2x))/x^4=#

#-πsin((x-1)/x^2)*(x^2-2x^2+2x)/x^4=#

#-πsin((x-1)/x^2)*(x(2-x))/x^4=#

#-πsin((x-1)/x^2)*(cancel(x)(2-x))/x^cancel(4)=#

#-πsin((x-1)/x^2)*(2-x)/x^3=#

#(π(x-2)sin((x-1)/x^2))/x^3#