Question

Помогите пожалуйста!
Найдите производную функций:
1.y=(x^2+2x+4)*(x-2)?
2. y= cosx*ctgx?
3.y=x^2 / 3-4x?
4. y=x / x^2+1?

Answer 1

1)$y'=(2x+2)(x-2)+(x^2+2x+4)= \ \ =2x^2-4x+2x-4+x^2+2x+4=3x^2$

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2) $y= cosxfrac{cosx}{sinx} = frac{cos^2x}{sinx} = frac{1-sin^2x}{sinx} = frac{1}{sinx}-sinx \ \ y'= -frac{cosx}{sin^2x}-cosx =-cosx(1+ frac{1}{sin^2x})$

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3)$y= frac{x^2}{3-4x} \ \ y'= frac{2x(3-4x)+4x^2}{(3-4x)^2} = frac{6x-8x^2-4x^2}{(3-4x)^2} = frac{6x(1-2x)}{(3-4x)^2}$

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