Question

найти dy

1)y=(ax^2+b)^3

2)y=arctg корень2x

Answer 1

$y=(ax^2+b)^3 ; \ dy=d((ax^2+b)^3)=\ 3(ax^2+b)^{3-1}d(ax^2+b)=\ 3(ax^2+b)^2 d(ax^2)=\ 3(ax^2+b)^2*a*2x dx=\ 6ax(ax^2+b)^2 dx$

 

$y=arctg sqrt{2x};\ dy=frac {1}{1+(sqrt{2x})^2}d (sqrt{2x})=\ frac{1}{1+2x}frac{1}{2sqrt{2x}}d (2x)=\ frac{1}{2(1+2x)sqrt{2x}} 2d x=\ frac{1}{(1+2x)sqrt{2x}} dx$