What is the derivative of $f (x) = π cos (\frac{x - 1}{x^{2}})$ $f(x)=picos((x-1)/x^2)$ ?

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Answer 1 · 2018-05-20T10:06:19

$(π(x-2)sin((x-1)/x^2))/x^3$

$f(x)=(πcos((x-1)/x^2))'$ $=$

$-πsin((x-1)/x^2)((x-1)/x^2)'=$

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

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

$-πsin((x-1)/x^2)*(x^2-2x^2+2x)/x^4=$

$-πsin((x-1)/x^2)*(x(2-x))/x^4=$

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

$-πsin((x-1)/x^2)*(2-x)/x^3=$

$(π(x-2)sin((x-1)/x^2))/x^3$

What is the derivative of f(x)=picos((x-1)/x^2)f(x)=πcos(x−1x2)f(x)=picos((x-1)/x^2)?