вправа 10.28 гдз 11 клас алгебра Істер 2019
Вправа 10.28
Знайдіть похідну функції:
1) у = 4√3х-1; 2) у = 5√7-3х; 3) у = √х2+7;
4) у = 1/(7√5х+11); 5) у = 9/(3√7х-1); 6) у = 1/(√х4-3).
1) у = 4√3х-1; 2) у = 5√7-3х; 3) у = √х2+7;
4) у = 1/(7√5х+11); 5) у = 9/(3√7х-1); 6) у = 1/(√х4-3).
Умова:
Відповідь ГДЗ:
1) у = 4√3х-1
у' = (4√3х-1)' = ((3х - 1)1/4)' = 1/4 • (3х - 1)1/4-1 • 3 =
= 3/4 • (3х - 1)-3/4 = 3/4 • 1/(4√(3х-1)3);
2) у = 5√7-3х
у' = (5√7-3х)' = ((7 - 3х)1/5)' = 1/5(7 - 3х)1/5-1 • (-3) =
= -3/5 • (7 - 3х)-4/5 = -3/5 • 1/(5√(7-3х)4) = - 3/(55√(7-3х)4);
3) у = √х2+7
у' = (√х2+7)' = 1/(2•√х2+7) • 2х = х/(√х2+7);
4) у = 1/(7√5х+11)
у' = (1/(7√5х+11))' = ((5х + 11)-1/7)' = 1/7 • (5х + 11)-1/7-1 • 5 =
= -5/7 • (5х + 11)-8/7 = - 5/(77√(5х+11)8);
5) у = 9/(3√7х-1)
у' = (9/(3√7х-1))' = 9 • ((7х - 1)-1/3)' = -9 • 1/3(7х - 1)-1/3-1 • =
= -3(7х - 1)-4/3 • 7 = -21 • (7х - 1)-4/3 = - 21/(3√(7х-1)4);
6) у = 1/(√х4-3)
у' = 1/(2√х4-3) • 4х3 = 2х3/(√х4-3).
у' = (4√3х-1)' = ((3х - 1)1/4)' = 1/4 • (3х - 1)1/4-1 • 3 =
= 3/4 • (3х - 1)-3/4 = 3/4 • 1/(4√(3х-1)3);
2) у = 5√7-3х
у' = (5√7-3х)' = ((7 - 3х)1/5)' = 1/5(7 - 3х)1/5-1 • (-3) =
= -3/5 • (7 - 3х)-4/5 = -3/5 • 1/(5√(7-3х)4) = - 3/(55√(7-3х)4);
3) у = √х2+7
у' = (√х2+7)' = 1/(2•√х2+7) • 2х = х/(√х2+7);
4) у = 1/(7√5х+11)
у' = (1/(7√5х+11))' = ((5х + 11)-1/7)' = 1/7 • (5х + 11)-1/7-1 • 5 =
= -5/7 • (5х + 11)-8/7 = - 5/(77√(5х+11)8);
5) у = 9/(3√7х-1)
у' = (9/(3√7х-1))' = 9 • ((7х - 1)-1/3)' = -9 • 1/3(7х - 1)-1/3-1 • =
= -3(7х - 1)-4/3 • 7 = -21 • (7х - 1)-4/3 = - 21/(3√(7х-1)4);
6) у = 1/(√х4-3)
у' = 1/(2√х4-3) • 4х3 = 2х3/(√х4-3).