求一道简单函数的导求f(x)=tanx/x的导!f(x)'=[x(secx)^2-tanx]/x^2=[x/(cosx)^2-sinx/cosx]/x^2=[x/(cosx)^2-sinxcosx/(cosx)^2]/x^2=(x-sinxcosx)/(x^2*(cosx)^2)可是书上答案是(x-sinx)/(x^2*(cosx)^2)我的求法不对么?
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![求一道简单函数的导求f(x)=tanx/x的导!f(x)'=[x(secx)^2-tanx]/x^2=[x/(cosx)^2-sinx/cosx]/x^2=[x/(cosx)^2-sinxcosx/(cosx)^2]/x^2=(x-sinxcosx)/(x^2*(cosx)^2)可是书上答案是(x-sinx)/(x^2*(cosx)^2)我的求法不对么?](/uploads/image/z/11460230-62-0.jpg?t=%E6%B1%82%E4%B8%80%E9%81%93%E7%AE%80%E5%8D%95%E5%87%BD%E6%95%B0%E7%9A%84%E5%AF%BC%E6%B1%82f%28x%29%3Dtanx%2Fx%E7%9A%84%E5%AF%BC%21f%28x%29%27%3D%5Bx%28secx%29%5E2-tanx%5D%2Fx%5E2%3D%5Bx%2F%28cosx%29%5E2-sinx%2Fcosx%5D%2Fx%5E2%3D%5Bx%2F%28cosx%29%5E2-sinxcosx%2F%28cosx%29%5E2%5D%2Fx%5E2%3D%28x-sinxcosx%29%2F%28x%5E2%2A%28cosx%29%5E2%29%E5%8F%AF%E6%98%AF%E4%B9%A6%E4%B8%8A%E7%AD%94%E6%A1%88%E6%98%AF%28x-sinx%29%2F%28x%5E2%2A%28cosx%29%5E2%29%E6%88%91%E7%9A%84%E6%B1%82%E6%B3%95%E4%B8%8D%E5%AF%B9%E4%B9%88%3F)
求一道简单函数的导求f(x)=tanx/x的导!f(x)'=[x(secx)^2-tanx]/x^2=[x/(cosx)^2-sinx/cosx]/x^2=[x/(cosx)^2-sinxcosx/(cosx)^2]/x^2=(x-sinxcosx)/(x^2*(cosx)^2)可是书上答案是(x-sinx)/(x^2*(cosx)^2)我的求法不对么?
求一道简单函数的导
求f(x)=tanx/x的导!
f(x)'=[x(secx)^2-tanx]/x^2=[x/(cosx)^2-sinx/cosx]/x^2
=[x/(cosx)^2-sinxcosx/(cosx)^2]/x^2
=(x-sinxcosx)/(x^2*(cosx)^2)
可是书上答案是(x-sinx)/(x^2*(cosx)^2)
我的求法不对么?
求一道简单函数的导求f(x)=tanx/x的导!f(x)'=[x(secx)^2-tanx]/x^2=[x/(cosx)^2-sinx/cosx]/x^2=[x/(cosx)^2-sinxcosx/(cosx)^2]/x^2=(x-sinxcosx)/(x^2*(cosx)^2)可是书上答案是(x-sinx)/(x^2*(cosx)^2)我的求法不对么?
f'(x)=(tanx/x)'
=[x(tanx)'-x'tanx]/x²
=(xsec²x-tanx)/x²
=(x/cos²x-sinx/cosx)/x²
=(x/cos²x-sinxcosx/cos²x)/x²
=(x-sin2x/2)/x²cos²x
=(2x-sin2x)/2x²cos²x
书上的答案肯定错!你的是对的,强烈的支持你!
书上不一定就是对的,“尽信书则不如无书”