Задача 1.Найти производные
1.1. y=37x+5−−−−−√+x+1−−−−−√54xy=37x+5+x+154x\displaystyle {y = \frac{3}{{\sqrt {7x + 5} }} + \frac{{\sqrt[5]{{x + 1}}}}{{4x}}}
1.5. y=3x2−arcsin1x;−−−√y=3x2−arcsin⁡1x;\displaystyle {y = 3{x^2} - \arcsin \sqrt {\frac{1}{x};} }
1.2. y=arctge−3x+2⋅ln2(1−6x2)y=arctge−3x+2⋅ln2⁡(1−6x2)\displaystyle {y = {\mathop{\rm arctg}\nolimits} {e^{ - 3x + 2}} \cdot \mathop {ln}\nolimits^2 (1 - 6{x^2})}
1.6. y=(5x2−8x+2)9⋅tg3x;y=(5x2−8x+2)9⋅tg3x;\displaystyle {y = (5{x^2} - 8x + {{2)}^9} \cdot tg3x;}
1.3. y=(ln2+3xx)√x+2y=(ln⁡2+3xx)x+2\displaystyle {y = {{\left( {\ln \frac{{2 + 3x}}{x}} \right)}^{\sqrt{}{{x + 2}}}}}
1.7. y=(lnx−5x−−√)sin32xy=(ln⁡x−5x)sin32x\displaystyle {y = (\ln x - 5\sqrt x {)^{{{\sin }^3}2x}}}
1.4. {x=ln1−t2−−−−−√,y=11−t2√;{x=ln⁡1−t2,y=11−t2;\displaystyle {\left\{ {\begin{array}{*{20}{l}}{x = \ln \sqrt {1 - {t^2}} ,}\\{y = \frac{1}{{\sqrt {1 - {t^2}} }};}\end{array}} \right.}
1.8. {x=ctg2t2,y=cos2t2+7.{x=ctg2t2,y=cos⁡2t2+7.\displaystyle {\left\{ {\begin{array}{*{20}{l}}{x = {\mathop{\rm ctg}\nolimits} \frac{2}{{{t^2}}},}\\{y = \cos \frac{2}{{{t^2}}} + 7.}\end{array}} \right.}