Ածանցյալ. առաջադրանքներ

Տնային առաջադրանքներ

(a) (i) y=x⁴, (x⁴)’=4x³
(ii) y=x, (x)’=0

(b) (i) y=3x⁷, (3x⁷)’=3*(x⁷)=3*7*x^7-1=21x⁶
(ii) y= -4x⁵, (-4x⁵)’=(-4)*x⁵=(-4)*5*x⁴=(-20x⁴)

(c) (i) y=10, (10)’=0
(ii) y= -3, (-3)’=0

(d) (i) y=4x³-5x²+2x-8
y’=4*3*x²-5*2*x+2*x-0=12x²-10x+2
(ii) y=2x⁴+3x³-x
y’=8x³+9x²-1

(e) (i) y=1/3x⁶
y’=(1/3)*6*x⁵=2x⁵
(ii) y=(-3/4x²)
y’=(-6/4x)=(-1,5x)

(f) (i) y=7x-(1/2)x³
y’=7-1,5x²
(ii) y=2-5x⁴+(1/5)x⁵
y’=(-20x³)+x⁴

(g) (i) y=x^3/2
y’=3/2*√x
(ii) y=x^2/3
y’=2/3x^(-1/3)=2/(3³√x)

(h) (i) y=6x^4/3
y’=8x^1/3=8³√x
(ii) y=3/5x^5/6
y’=(3/5)*(5/6)*x^(-1/6)=3/6x^(-1/6)=1/2⁶√x

(i) (i) y=3x⁴-x²+15x^2/5-2
y’=12x³-2x+6/⁵√x³
(ii) y=x³-3/5x^5/3+4/3x^1/2
y’=3x²-x^2/3+2/3x^(-1/2)=3x²—³√x²+2/3√x

(j) (i) y=(x^-1)
y’= (-1/x²)
(ii) y=(-x^-3)
y’==3/x⁴

(k) (i) y=x^(-1/2)
y’=(-1/2)x^(-1/2)-1=(-1/2)x^(-3/2)=(-1/2√x³)
(ii) y= -8x^(-3/4)
y’=6x^(-3/4)-1=6*x^(-7/4)=6/x^(7/4)=6/⁴√x⁷

(l) (i) y=5x-8/15x^5/2
y’=5-(8/15)*(5/2)*x^3/2=5-4/3x^3/2
(ii) y= -7/3x^3/7+4/3x^(-6)
y’= -7/3*3/7*x^(-4/7)+4/3*x^(-6)= (-1/⁷√x⁴)-(8/x⁷)