写出来这题的详细过程，步骤都写出来，谢谢
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dy/dx=(dy/dt)/(dx/dt)
=(e^t·cost)'/(e^t·sint)'
=(e^t·cost-e^t·sint)/(e^t·sint+e^t·cost)
=(cost-sint)/(sint+cost)
dy/dx|t=π/2
=(cosπ/2 -sinπ/2)/(sinπ/2 +cosπ/2)
=(0-1)/(1+0)
=-1
=(e^t·cost)'/(e^t·sint)'
=(e^t·cost-e^t·sint)/(e^t·sint+e^t·cost)
=(cost-sint)/(sint+cost)
dy/dx|t=π/2
=(cosπ/2 -sinπ/2)/(sinπ/2 +cosπ/2)
=(0-1)/(1+0)
=-1
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