Question

Найти производные функций

Answer 1

$y = \dfrac{3x^2}{x^2+5}\\\\\\y' = \dfrac{(3x^2)'(x^2+5) - 3x^2(x^2+5)'}{(x^2+5)^2} = \dfrac{6x(x^2+5)- 3x^2\cdot 2x}{(x^2+5)^2} = \dfrac{6x^3 + 30x - 6x^3}{(x^2+5)^2} =\\\\\\= \boxed{\bf{\dfrac{30x}{\left(x^2+5\right)^2}}}$

$y = e^{5x+3}\\\\\\y' = (5x+3)' \cdot e^{5x+3} = \boxed{\bf{5e^{5x+3}}}$