求下列函数的导数.①y=(2x²+3)(3x-1); ②y=(√x-2)²; ③y=x-sin(x/2)cos(x/2); ④y=[ln(2x+3)]/x²+1.
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![求下列函数的导数.①y=(2x²+3)(3x-1); ②y=(√x-2)²; ③y=x-sin(x/2)cos(x/2); ④y=[ln(2x+3)]/x²+1.](/uploads/image/z/1698937-25-7.jpg?t=%E6%B1%82%E4%B8%8B%E5%88%97%E5%87%BD%E6%95%B0%E7%9A%84%E5%AF%BC%E6%95%B0.%E2%91%A0y%3D%EF%BC%882x%26%23178%3B%2B3%EF%BC%89%EF%BC%883x-1%EF%BC%89%3B+%E2%91%A1y%3D%EF%BC%88%E2%88%9Ax-2%EF%BC%89%26%23178%3B%3B+%E2%91%A2y%3Dx-sin%EF%BC%88x%2F2%EF%BC%89cos%EF%BC%88x%2F2%EF%BC%89%3B+%E2%91%A3y%3D%EF%BC%BBln%EF%BC%882x%2B3%EF%BC%89%EF%BC%BD%2Fx%26%23178%3B%2B1.)
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求下列函数的导数.①y=(2x²+3)(3x-1); ②y=(√x-2)²; ③y=x-sin(x/2)cos(x/2); ④y=[ln(2x+3)]/x²+1.
求下列函数的导数.①y=(2x²+3)(3x-1); ②y=(√x-2)²; ③y=x-sin(x/2)cos(x/2); ④y=[ln(2x+3)]/x²+1.
求下列函数的导数.①y=(2x²+3)(3x-1); ②y=(√x-2)²; ③y=x-sin(x/2)cos(x/2); ④y=[ln(2x+3)]/x²+1.
求下列函数的导数
(1) y=(2x²+3)(3x-1)
y=(2x²+3)(3x-1)=6x³-2x²+9x-3,故y′=18x²-4x+9
(2) y=√(x-2)²
y=√(x-2)²=︱x-2︱
当x≧2时,y=x-2,此时y′=1;当x≦2时,y=-(x-2)=-x+2,此时y′=-1.
(3) y=x-sin(x/2)cos(x/2)
y′=x′-{[sin(x/2)]′cos(x/2)+sin(x/2)[cos(x/2)]′}
=1-{[cos(x/2)](x/2)′cos(x/2)+sin(x/2)[-sin(x/2)](x/2)′}
=1-[(1/2)cos²(x/2)-(1/2)sin²(x/2)]=1-(1/2)[cos²(x/2)-sin²(x/2)]=1-(1/2)cosx
注“为什么(3x)'=3?”是因为(3x)′=3′x+3x′=0×x+3×1=3
常量的导数=0,即c′=0,3是常量,故3′=0;(xⁿ)′=nxⁿֿ¹.