Question

Найдите производную функции
f(x)=√3x+2+x^4
f(x)=(-x²+2x)³+(x+3)^4
f(x)=√7+14x-5x^6
f(x)=(-4x³+1)^4-(2-x)^5

Answer 1

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