Question

Найти производную.....

Answer 1

y' = (e^(3x+15x^2))' = e^(3x+15x^2)* (3x+15x^2)' = e^(3x+15x^2)*(3+30x)

y' = (e^3x)' * cos^2 (5x) + e^3x * (cos^2 5x)' = e^3x * (3x)' * cos^2 5x + e^3x * 2cos5x * (cos5x)' = 3*e^3x *cos^2 5x + 2*e^3x * cos5x * (-sin5x) * (5x)' = 3*e^3x *cos^2 5x - 2*e^3x * cos5x * sin5x * 5

Answer 2

$boxed {1.}; ; ; y=e^{3x+15x^2}\\y'=e^{3x+15x^2}cdot (3x+15x^2)'=e^{3x+15x^2}cdot (3+30x)\\boxed {2.}; ; ; y=e^{3x}cdot cos^25x\\y'=e^{3x}cdot (3x)'cdot cos^25x+e^{3x}cdot 2cdot cos5xcdot (cos5x)'=\\=e^{3x}cdot 3cdot cos^25x+e^{3x}cdot 2cdot cos5xcdot (-sin5x)cdot 5=\\=3e^{3x}cdot cos^25x-5cdot sin10x$