Question

Найдите производную функций:
a) $f(x)= sqrt{7+14x} -5 x^{6}$
b) $f(x)=(-4 x^{3} +1)^{4} -(2-x)^{5}$

Answer 1

$f(x) = sqrt{7+14x} -5 x^{6}\\f'(x)=( sqrt{7+14x})' -5( x^{6})'= frac{1}{2 sqrt{7+14x} }*(7+14x)' - 5*6 x^{5}=$$frac{14}{2 sqrt{7+14x} } -30 x^{5} = frac{7}{ sqrt{7+14x} }-30 x^{5}\\ f(x)=(-4 x^{3} +1) ^{4} -(2-x) ^{5}\\f'(x)=[(-4 x^{3}+1) ^{4}]' - [(2-x) ^{5} ]'= 4(-4 x^{3}+1) ^{3}*(-4 x^{3}+1)'-$$5(2-x) ^{4}*(2-x)' =4*(-12 x^{2} )(-4 x^{3}+1) ^{3}+5(2-x) ^{4} =$$-48 x^{2} (-4 x^{3}+1) ^{3} +5(2-x) ^{4}$

Answer 2

Огромное Вам спасибо. =)

Answer 3

Пожалуйста ))