Բանաձևեր՝
(f*g)’=f’*g+g’*f
(f/g)’=(f’*g-g’*f)/g2
Առաջադրանք 256
ա) f(x)=(2x-1)/1-x
f'(x)=2, g'(x)=(-1)
f'(x)=(2*(1-x)+(-1)*(2x-1))/(1-x)2
f'(x)=(2-2x+(-2x)+1)/x2-2x+1=(3-4x)/x2-2x+1
բ) f(x)=(2x2-4)/x+1
f'(x)=4x, g'(x)=1
f'(x)=(4x*(x+1)-1*(2x2-4))/(x+1)2=(2x2+4x+4)/(x+1)2
Առաջադրանք 257
ա) f(x)=(3-4x)/x2
f'(x)= -4, g'(x)=2x
f'(x)=((-4)x2-2x(3-4x))/(x2)2=(-2*(-2x+3))/x3
բ) f(x)=(x2+1)/√x
f'(x)=2x, g'(x)=1/2√x
f'(x)=(2x*√x-(1/2√x)*(x2+1))/(√x)2=(3x2-1)/2x√x
Առաջադրանք 258
ա) f(x)=(x4-x)/x2
f'(x)=4x3-1, g'(x)=2x
f'(x)=((4x3-1)x2-2x*(x4-x))/(x2)2=(2x3+1)/x2
բ) f(x)=(5-2x6)/1-x3
f'(x)= -12x5, g'(x)= -3x2
f'(x)=((-12x5)*(1-x3)-(-3x2)*(5-2x6))/(1-x3)2=(6x8-12x5+15x2)/(1-x3)2
Առաջադրանք 259
ա) f(x)=(√x+1)/x3
f'(x)=1/2√x, g'(x)=3x2
f'(x)=(1/2√x)x3-3x2*(√x+1))/(x3)2=(x5/2-6x2*(√x+1))/2x6
բ) f(x)=(x3-1)/(x2-1)
f'(x)=3x2, g'(x)=2x
f'(x)=(3x2*(x2-1)-2x*(x3-1))/(x2-1)2=(x*(x+2))/(x+1)2
Առաջադրանք 263
ա) f(x)=(1-2x)/(x2+1)
f'(x)= -2, g'(x)=2x
f'(x)=(2x2-2x-2)/(x2+1)2
f'(x)=0
f'(x)= -2
բ) f(x)=(x2+2x)/(1-x)
f'(x)=2x+2, g'(x)= -1
f'(x)=(-x2+2x+2)/(1-x)2
f'(x)=0
f'(x)=2
գ) f(x)=(x+1)/(x2+2x+3)
f'(x)=1, g'(x)=2x+2
f'(x)=(-x2-2x+1)/(x2+2x+3)2
f'(x)=0
f'(x)=1/9
դ) f(x)=(2-x)/(x2-3x+4)
f'(x)= -1, g'(x)=2x-3
f'(x)=(x2-4x+2)/(x2-3x+4)2
f'(x)=0
f'(x)=1/8
Դավիթ Մուրադյան 