求下列函数的导数:(1)y=sin^4(π/4)+cos^4(π/4); (2)y=(1+√x)/(1-√x)+(1-√
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求下列函数的导数:(1)y=sin^4(π/4)+cos^4(π/4); (2)y=(1+√x)/(1-√x)+(1-√x)/(1+√x)
第一题是否未写自变量?若没有自变量,就是常数,其导数为 0;若有自变量,求导如下:
y=sin^4(πx/4)+cos^4(πx/4)
y'=4 sin^3(πx/4) cos(πx/4) π/4 + 4 cos^3(πx/4) [-sin(πx/4)] π/4
= π sin(πx/4) cos(πx/4) [sin^2(πx/4)- cos^2(πx/4)]
= - π/2 sin(πx/2) cos(πx/2)
= - π/4 sin(πx)
y=(1+√x)/(1-√x)+(1-√x)/(1+√x)
=[(1+√x)²+(1-√x)²] / [(1-√x)(1+√x)]
=(1+2√x+x+1-2√x+x) / (1-x)
= 2(1+x)/(1-x)
=4/(1-x) - 2
y'= -4/(1-x)² (-1) = 4/(1-x)²
再问: 话说导数是什么呢??怎么感觉没学过。。。。
y=sin^4(πx/4)+cos^4(πx/4)
y'=4 sin^3(πx/4) cos(πx/4) π/4 + 4 cos^3(πx/4) [-sin(πx/4)] π/4
= π sin(πx/4) cos(πx/4) [sin^2(πx/4)- cos^2(πx/4)]
= - π/2 sin(πx/2) cos(πx/2)
= - π/4 sin(πx)
y=(1+√x)/(1-√x)+(1-√x)/(1+√x)
=[(1+√x)²+(1-√x)²] / [(1-√x)(1+√x)]
=(1+2√x+x+1-2√x+x) / (1-x)
= 2(1+x)/(1-x)
=4/(1-x) - 2
y'= -4/(1-x)² (-1) = 4/(1-x)²
再问: 话说导数是什么呢??怎么感觉没学过。。。。
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