y = sec (x) + csc (x) 求导,之后代入x = 3pi / 4 求值,要较详细步骤!如题无误!

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y=sec(x)+csc(x)求导,之后代入x=3pi/4求值,要较详细步骤!如题无误!y=sec(x)+csc(x)求导,之后代入x=3pi/4求值,要较详细步骤!如题无误!y=sec(x)+csc

y = sec (x) + csc (x) 求导,之后代入x = 3pi / 4 求值,要较详细步骤!如题无误!
y = sec (x) + csc (x) 求导,之后代入x = 3pi / 4 求值,要较详细步骤!
如题无误!

y = sec (x) + csc (x) 求导,之后代入x = 3pi / 4 求值,要较详细步骤!如题无误!
y'=secxtanx+(-cscxcotx)
=secxtanx-cscxcotx
x=3π/4
y'=(-√2)*(-1)-√2*(-1)=2√2
求导过程
(secx)'=[(cosx)^-1]'
=-1*(cosx)^-2*(cosx)'
=-(cosx)^-2*(-sinx)
=sinx/cosx*1/cosx
=secxtanx
(cscx)'同理可得

y' = (sec(x))' + (csc(x))'
=tan(x)sec(x) - cot(x) csc(x)
带入x= 3π/4有
y' = -1 * (-根号2) - (-1) * (根号2)
=2根号2