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

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