z=u²v+3uv^4,u=e^x, v=sin x,求dz/dx,求各位大神解答啊→_→
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![z=u²v+3uv^4,u=e^x, v=sin x,求dz/dx,求各位大神解答啊→_→](/uploads/image/z/8772429-21-9.jpg?t=z%3Du%26%23178%3Bv%2B3uv%5E4%2Cu%3De%5Ex%2C+v%3Dsin+x%2C%E6%B1%82dz%2Fdx%2C%E6%B1%82%E5%90%84%E4%BD%8D%E5%A4%A7%E7%A5%9E%E8%A7%A3%E7%AD%94%E5%95%8A%E2%86%92_%E2%86%92)
z=u²v+3uv^4,u=e^x, v=sin x,求dz/dx,求各位大神解答啊→_→
z=u²v+3uv^4,u=e^x, v=sin x,求dz/dx,求各位大神解答啊→_→
z=u²v+3uv^4,u=e^x, v=sin x,求dz/dx,求各位大神解答啊→_→
z=u²v+3uv^4,u=e^x,v=sin x,求dz/dx
dz/dx=2uu'v+u^2v'+3u'v^4+3v(4v^3)v'
=2e^(2x)sinx + e^(2x)cosx +3e^x (sinx)^4 + 12(sinx)^4 cosx
=2sinx e^(2x) + cosx e^(2x) + 3(sinx)^4 e^x (e^x + 4cosx)
=2sinx e^(2x) + 3(sinx)^4 e^(2x) + cosx e^(2x)+12(sinx)^4 cosx e^(x)
=sinx e^(2x)[2+3(sinx)^3] + cosx e^x [e^x+12(sinx)^4]