Найти производную второго порядка от функции заданной параметрически x=e^t sint y=e^t cost

[latex]\frac{dy}{dx}=-\frac{dy}{dt}:\frac{dx}{dt}[/latex] [latex]\frac{dx}{dt}=e^tsint+e^tcost[/latex] [latex]\frac{dy}{dt}=e^tcost-e^tsint[/latex] [latex]\frac{dy}{dx}=-\frac{e^tcost-e^tsint}{e^tsint+e^tcost}=\frac{cost-sint}{sint+cost}[/latex] [latex]\frac{d^2y}{dx^2}=(-\frac{cost-sint}{sint+cost})'=-\frac{(-sint-cost)(sint+cost)-(cost-sint)(cost-sint)}{(sint+cost)^2}[/latex] [latex]\frac{d^2y}{dx^2}=-\frac{-(sint+cost)^2-(cost-sint)^2}{(sint+cost)^2}=\frac{(sint+cost)^2+(cost-sint)^2}{(sint+cost)^2}[/latex]