设dy/dx∫(0,e^-x)f(t)dt=e^x,f(x)=?

设dy/dx∫(0,e^-x)f(t)dt=e^x,f(x)=? 设x=e^(-t) 试变换方程x^2 d^2y/dx^2 +xdy/dx+y=0网上有种解法如下（网友franciscococo提供）：x=e^(-t),即dx/dt= -e^(-t)那么dy/dx=(dy/dt) / (dx/dt)= -e^t *dy/dt,而d^2y/dx^2= [d(dy/dx) /dt] * dt/dx= [-e^t *d^2y/dt^2 -e^t *dy/dt] * ( 设f(x)连续,Y=∫0~X tf（x^2-t^2）dt 则dy/dx=? 设x=e^(-t),变换方程x^2*d^2y/dx^2+x*dy/dx+y=0设x=e^(-t),变换方程(x^2)*d^2y/dx^2+x*dy/dx+y=0答案是d^x/dt^2+y=0 设f(t)是二次可微函数且f''(t)不等于0 x=f'(t),y=tf'(t)-f(t),求dy/dx,d^2y/dx^2 设函数y=y(x)由x=1-e^t和y=t+e^-t确定,求dy/dx和d^2y/dx^2 数学题求dy/dx设 f'(x)=sin√x 定义（x>0）,又y=f[e^(2x)]求dy/dx d(t(dy/dt))/dx为什么等于t² d²y/dt²+t dy/dt作变量代换x=lnt简化方程d^2y/dx^2-dy/dx+e^2x*y=0x=lntdx/dt=1/tdy/dx=(dy/dt)/(dx/dt)=t dy/dtd²y/dx²=[d/dt(dy/dx)]/(dx/dt)=t² d²y/dt²+t dy/dt代入d^2y/dx^2- 设参数方程x=2t^3+2,y=e^2t 确定函数x=x(y),求dx/dy,d^2x/dy^2 设f(x)= ∫0-x e^(-y+2y)dy 求∫0-1 [(1-x)^2]f(x)dx 设x=e'sin t,y=e'cos t,求dy/dx. 设x=e^-t y=e^-2t 求dy/dx 设x=3e^-t,y=2e^t,则dy/dx等于多少? 设x=3e^-t,y=2e^t,则dy/dx等于多少? 设 {x=2t^3+2 y=e^2t-1 ,求dy/dx,d^2y/dx^2 设y=f(e^3x),f'(x)=lnx,则dy|dx等于多少, 设函数y=f(x)由方程sin(xy)+e^(x+y)=0确定,求dy/dx 由参数方程确定的函数的求导公式设x=G(t) y=F(t) d²y/dx²=d/dx(dy/dx)=d/dx [G'(t)/F'(t) ]=d/dt[G'（t)/F'(t)] dt/dx 尤其是d/dx d/dt 的符号意思