Question

Найдите производную функции F(x) =(x^2+3x)√x
Вычислите:
f'(1/4)

Answer 1

$f(x)=(x^2+3x)\sqrt x\\\\f'(x)=(x^2+3x)'\cdot\sqrt x+(x^2+3x)\cdot(\sqrt x)'=(2x+3)\sqrt x+\frac{x^2+3x}{2\sqrt x}=\\\\=\frac{(2x+3)2x+x^2+3x}{2\sqrt x}=\frac{4x^2+6x+x^2+3x}{2\sqrt x}=\frac{5x^2+9x}{2\sqrt x}\\\\\\f'\left(\frac14\right)=\frac{5\cdot\frac1{16}+9\cdot\frac14}{2\cdot\frac12}=\frac5{16}+\frac94=\frac{41}{16}=2\frac9{16}$