Question

найти производную:
y= ((x^2-1)/(x^2+1))^4

Answer 1

$y=(\frac{x^{2}-1} {x^{2}+1}) ^{4}\\y'=4*(\frac{x^{2}-1} {x^{2}+1}) ^{3}*( \frac{x^{2}-1} {x^{2}+1})'=4*(\frac{x^{2}-1} {x^{2}+1}) ^{3}* \frac{(x^{2}-1)'*(x^{2}+1)-(x^{2}-1)*(x^{2}+1)'}{(x^{2}+1) ^{2}}=4*( \frac{x^{2}-1} {x^{2}+1}) ^{3}* \frac{2x(x^{2}+1)-2x(x^{2}-1)}{(x^{2}+1) ^{2}}=4*( \frac{x^{2}-1} {x^{2}+1}) ^{3}*\frac{2x(x^{2}+1-x^{2}+1)}{(x^{2}+1)^{2}}= \frac{16x(x^{2}-1)^3} {(x^{2}+1) ^{5}}$