微积分练习题

1.dy/dx=2x+9/(x^2)
2.dy/dx=2x+2-2/(x-1)^3
3.y=(x+2)(x+3)/x+1
dy/dx=1-6/x^2
4.F'(x)=f'(x)g(x)+f(x)g'(x)
F'(1)=f'(1)g(1)+f(1)g'(1)=2*5+3*4=22
G'(x)=(f'(x)g(x)-g'(x)f(x))/g(x)^2
G'(1)=(f'(1)g(1)-g'(1)f(1))/g(1)^2=(2*5-4*3)/5^2=-2/25
5.dy/dx=dy/dz * dz/dx
=(z^2+1)^2(7z^2+1)*2(x+1) (再带入z=(x+1)^2)
=2(x+1)[(x+1)^4+1][7(x+1)^4+1]

1.
dy/dx=2x+9/x^2

2.
y=x^2+2x+1/(x-1)^2
dy/dx=2x+2-2/(x-1)^3

3.
y=(x^2+5x+6)/x+1=x+5+6/x+1
dy/dx=1-6/x^2

4.
F'(1)=f(1)g'(1)+f'(1)g(1)
=3*4+5*2=22

5.
太麻烦了，不想算了。