Question

найдите производную
1. y = 5x^2 - 2x^3 + (3/5x) - 7
2. y = (2 корень из x) + 12 sinx - 3tgx
3. y = (корень из x) (5x-3)
4. y = x/(x^2+1)

Answer 1

=========== 1 ===========
$y=5x^2 - 2x^3 + frac{3}{5}x - 7\ y'=(5x^2 - 2x^3 + frac{3}{5}x - 7)'=(5x^2)' - (2x^3)' + (frac{3}{5}x)' - (7)'=\ =10x-6x^2+ frac{3}{5}$
=========== 2 ===========
$y = 2 sqrt{x} + frac{1}{2} sinx - 3tgx\ y'=(2 sqrt{x} + frac{1}{2} sinx - 3tgx)'=(2 sqrt{x})' + (frac{1}{2} sinx)' - (3tgx)'=\ = frac{1}{ sqrt{x} } +frac{1}{2}cosx- frac{3}{cos^2x}$
=========== 3 ===========
$y= sqrt{x} cdot (5x-3)\ y'=(sqrt{x} cdot (5x-3))'=(sqrt{x})' cdot (5x-3)+sqrt{x} cdot (5x-3)'=\ = frac{5x-3}{2 sqrt{x} } +5 sqrt{x}$
=========== 4 ===========
$y= frac{x}{x^2+1} \ y'=(frac{x}{x^2+1})'=frac{(x)'cdot (x^2+1)-xcdot(x^2+1)'}{(x^2+1)^2}= frac{x^2+1-xcdot2x}{(x^2+1)^2}= frac{1-x^2}{(x^2+1)^2}$