大哥些帮忙做几倒导数的数学题`谢谢啊

来源：百度知道 编辑：UC知道 时间：2024/05/31 22:21:35
(1).y=x^4 (2).y=x^2的立方根 (3).y=x^3乘x的5次方根
(4).y=1/x^2 (5).y=2x^2-3x+1 (6).y=x^2sinx (7).y=1/x^3
(8).y=(x^2+2x+5)e^x (9).y=e^xsinx (10).y=(2x+5)^4
(11).y=sin(5x+π/4) (12).y=e^x^2

(1).y=x^4
y'=4*x^(4-1)
=4x^3

(2).y=x^2的立方根
=x^2^(1/3)
=x^(2/3)
y'=(1/3)x^(-1/3)
=1/(3*x的立方根)

(3).y=x^3乘x的5次方根
=x^(3+1/5)
=x^(16/5)
y'=(16/5)*x^(11/5)

(4).y=1/x^2
=x^(-2)
y'=-2x^(-3)=-2/x^3

(5).y=2x^2-3x+1
y'=4x-3

(6).y=x^2sinx
y'=(x^2)'sinx+x^2(sinx)'
=2xsinx+x^2cosx

(7).y=1/x^3
=x^(-3)
y'=-3x^(-4)
=-3/x^4

(8).y=(x^2+2x+5)e^x
y'=(x^2+2x+5)'e^x+(x^2+2x+5)(e^x)'
=(2x+2)e^x+(x^2+2x+5)e^x
=(2x+2+x^2+2x+5)e^x
=(x^2+4x+7)e^x

(9).y=e^xsinx
y'=(e^x)'sinx+e^x(sinx)'
=e^xsinx+e^xcosx
=e^x(sinx+cosx)

(10).y=(2x+5)^4
y'=4(2x+5)^3*(2x+5)'
=8(2x+5)^3

(11).y=sin(5x+π/4)
y'=cos(5x+π/4)*(5x+π/4)'
=5cos(5x+π/4)

(12).y=e^(x^2)
y'=e^(x^2)*(x^2)'
=2xe^