Question

найти производные следующих функций 
y=3
y=x
y=4x
y=x^4
y=5x^5
y=2x^4+2/3x^3+1/2
y=(4x^3-4)(4x^2-4)
y=3x^2/(x+3)

Answer 1

$1) y'=3' = 0 \ \ 2) y'=x' = 1 \ \ 3) y'=(4x)' = 4$

$4) y'=(x^4)' = 4 x^{3} \ \ 5) y'=(5x^5)' = 25 x^{4} \ \ 6) y'=(2x^4+2/3x^3+1/2)' = (2x^4)'+(2/3x^3)'+(1/2)' =8 x^{3}+2 x^{2}$

$7) y'=((4x^3-4)(4x^2-4))' = \ \ = (4x^3-4)'(4x^2-4)+(4x^3-4)(4x^2-4)'= \ \ = 12x^2*(4x^2-4)+8x*(4x^3-4)$

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