sin+3+x+的导数是什么

赵超詹1705sin(x^2+x+1)的导数?为什么答案不是cos(x^2+x+1)*(2x+1)? -
农士河15086086525 ______[答案] 此类复合函数求导,应由外向内,逐次求导并相乘. [sin(x^2+x+1)]' =[cos(x^2+x+1)](2x+1)

赵超詹1705复合函数导数例子:y(x)=sin(2x+3)的导数可以这样求:设u=2x+3,则可以用y'(x)=y'(u)* u' 这个公式是怎么推来的呢? -
农士河15086086525 ______[答案] F'(g(x)) = [ F(g(x+dx)) - F(g(x)) ] / dx .(1) g(x+dx) - g(x) = g'(x)*dx = dg(x) .(2) g(x+dx) = g(x) + dg(x) .(3) F'(g(x)) = [ F(g(x) + dg(x)) - F(g(x)) ] /dx = [ F(g(x) + dg(x)) - F(g(x)) ] / dg(x) * dg(x)/dx = F'(g) * g'(x)

赵超詹1705sin^2(x+3)的导数是 sin*2(x+3)是怎么求的 -
农士河15086086525 ______[答案] [sin^2(x+3)]' =2sin(x+3)*[sin(x+3)]' =2sin(x+3)*cos(x+3)

赵超詹1705(sin(1+2x)/x)导数是(2xcos(1+2x) - sin(1+x))/X的平方 为什么不是(xcos(1+2x) - sin( -
农士河15086086525 ______[答案] sin(1+2x)/x=sin(1+2x)*(x^(-1)) (sin(1+2x)/x)'=[sin(1+2x)*(x^(-1))]'= =cos(1+2x)(2)*(x*(-1))+sin(1+2x)*(-1/x^2)= =[2xcos(1+2x)-sin(1+2x)]/x^2

赵超詹1705y=sin(x)^3+sin(x^3)的复合导数咋求的?求教是sinx/的3次方加上sin/x的3次方 -
农士河15086086525 ______[答案] y'=3sinx^2*cosx+cosx^3*3x^2

赵超詹1705 求函数y=sin[cos(x 3 +x)]的导数. -
农士河15086086525 ______[答案] y′=cos[cos(x 3 +x)]·[cos(x 3 +x)]′ =cos[cos(x 3 +x)]·[-sin(x 3 +x)]·(x 3 +x)′ =cos[cos(x 3 +x)]·[-sin(x 3 +x)]·(3x 2 +1)...

赵超詹1705求(√1+sin^2x)cosx的二阶导数.要过程. -
农士河15086086525 ______ 原式一阶导数=(√1+sin^2x)' cosx+(√1+sin^2x)(-sinx) =[1/2*(1+sin^2x)^(-1/2)*(2*sinx)*cosx]*cosx-(√1+sin^2x)*sinx =sinx*cosx*cosx*(1+sin^2x)^(-1/2)-(√1+sin^2x)*sinx =sinx*[cos^2 x -(1+sin^2x)]/(1+sin^2x)^(1/2) =sinx*[cos^2 x -1-sin^2x)]/(1+...

赵超詹1705求f(x)=sin3xcos2x的n阶导数,尽量详尽,谢谢! -
农士河15086086525 ______[答案] f(x)=sin3xcos2x=1/2[sin5x+sinx] sinx的n阶导数=sin(x+nπ/2) 【理由:(sinx)'=cosx=sin(x+π/2), (sinx)''=(sin(x+π/2))'=cos(x+π/2)=sin(x+2*π/2), ...以此类推】 sin5x的n阶导数=5^(n)sin(5x+nπ/2) f(x)=sin3xcos2x的n阶导数=1/2(5^(n)sin(5x+nπ/2)+sin(x...

赵超詹1705 求下列各函数的导数:(1)y= ;(2)y=(x+1)(x+2)(x+3);(3)y= - sin (1 - 2cos 2 );(4)y= + . -
农士河15086086525 ______[答案] (1)-x+3x2-2x-3sinx+x-2cosx. (2)3x2+12x+11 (3)cosx (4) (1)∵y==x+x3+, ∴y′=(x)′+(x3)′+(x-2sinx)′ =-x+3x2-2x-3sinx+x-2cosx.... =(2x+3)(x+3)+(x+1)(x+2) =3x2+12x+11. (3)∵y=-sin(-cos)=sinx, ∴y′=(sinx) ′=(sinx)′=cosx. (4)y=+==, ∴y′=()′==.

赵超詹1705求(√1+sin^2x)cosx的二阶导数. -
农士河15086086525 ______[答案] 原式一阶导数=(√1+sin^2x)' cosx+(√1+sin^2x)(-sinx) =[1/2*(1+sin^2x)^(-1/2)*(2*sinx)*cosx]*cosx-(√1+sin^2x)*sinx =sinx*cosx*cosx*(1+sin^2x)^(-1/2)-(√1+sin^2x)*sinx =sinx*[cos^2 x -(1+sin^2x)]/(1+sin^2x)^(1/2) =sinx*[cos^2 x -1-sin^2x)]/(1+sin^2x)...