Question

求由方程e的xy次方=2x+y的3次方所确定的隐函数y=f(x)的微分dy.

急求 亲们 帮帮忙 能做几题做几题...谢了

Answer 1

3、e^(xy)=2x+y^3，两边取微分
d[e^(xy)]=d[2x+y^3]
ye^(xy)dx+xe^(xy)dy=2dx+3y^2dy
[xe^(xy)-3y^2]dy=[2-ye^(xy)]dx
dy=[2-ye^(xy)]/[xe^(xy)-3y^2]*dx
4、①∫x^4/(x^2+1)*dx
=∫(x^4+x^2-x^2-1+1)/(x^2+1)*dx
=∫x^2dx-∫dx+∫1/(x^2+1)*dx
=x^3/3-x+arctanx+C
②∫x^2lnxdx
=1/3∫lnxd(x^3)
=1/3*lnx*x^3-1/3∫x^3dlnx
=1/3*lnx*x^3-1/3∫x^2dx
=1/3*lnx*x^3-1/3*x^3/3+C
=x^3/9*(3lnx-1)+C
5、f(x)=x^3/3-x^2-3x
f'(x)=x^2-2x-3
x≤-1或x≥3时，f'(x)≥0，∴单调增区间为(-∞,-1]∪[3,+∞)
-1≤x≤3时，f'(x)≤0，∴单调减区间为[-1,3]
由单调区间知，x=-1时，取得极大值f(-1)=-1/3-1+3=5/3
x=3时，取得极小值f(3)=3^2-3^2-3*3=-9
f''(x)=2x-2
x≤1时，f''(x)≤0，∴凸区间为(-∞,1]
x≥1时，f''(x)≥0，∴凹区间为[1,+∞)
f''(x)=0时为拐点，此时 x=1，f(1)=1/3-1-3=-11/3
∴拐点为(1,-11/3)

Answer 2

哥你考试来吧，看不懂的啊，你后面的是（2x+y)的三次方还是y的三次方啊？