Question

求下列高数的导数

写的越详细越好

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Answer 1

有些简单运算自己去完成

Answer 2

y'=e^-(sin1/x)^2 *2*sin1/x*cos1/x*1/x^2
y'=(scs(ln(1+x^2))^2*1/(1+x^2)*2x

追问

没了？

Answer 3

1.y=e^[-sin² (1/x)] y'=e^[-sin² (1/x)] [-2sin(1/x)cos(1/x)(-1/x²)]=-(1/x²)sin(2/x) e^[-sin² (1/x)]
2.y=tan [ln(1+x²)] y'=sec²[ln(1+x²)] [2x/(1+x²)] = 2xsec²[ln(1+x²)]/(1+x²)
3.y=x^(x^2) lny =x^2 lnx d(lny)/dx = y'/y = 2xlnx+x y'=x(2lnx + 1)x^(x^2) = (2lnx + 1)x^(x²+1)
4. cos(xy) = x² y² 求y的dy：
-sin(xy) (y+xy') = 2xy²+x² (2yy') -ysin(xy)-xy'sin(xy) = 2xy² + 2x²yy'
y'[xsin(xy)+2x²y] = -y[sin(xy) + 2xy]
解出：y' = -y[sin(xy) + 2xy] / x[sin(xy)+2xy] = -y/x
从而： dy = - y dx / x 或写成：
x dy = - y dx
其它题略（见谅）