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Ответ:

Производная произведения равна  [tex]\bf (uv)'=u'v+uv'[/tex]  .

[tex]y=sh^23x+arcctg\, (5x^2)\ \ ,\\\\\\\boldsymbol{(u^2)'=2u\cdot u'\ \ ,\ \ (shu)'=chu\cdot u'\ \ ,\ \ (arcctgu)'=-\dfrac{1}{1+u^2}\cdot u'}\\\\\\y'=2\cdot sh3x\cdot (sh3x)'-\dfrac{1}{1+(5x^2)^2}\cdot (5x^2)'=\\\\\\=\bf 2\cdot sh3x\cdot ch3x\cdot 3-\dfrac{1}{1+25x^4}\cdot 10x[/tex]