已知函数f(x)= f'(π/4)cosx+sinx,则f(π/4)的值
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f'(π/4) 是一个确定的 常数了,不要被误导了
f(x)求导得到
f'(π/4)
=-f'(π/4)*sin(π/4)+cos(π/4)
=-f'(π/4)*√2/2+√2/2
(1+√2/2)f'(π/4)=√2/2
f'(π/4)=√2/2/(1+√2/2)=√2/(2+√2)
f(π/4)
=f'(π/4)*cos(π/4)+sin(π/4)
=f'(π/4)*√2/2+√2/2
=(f'(π/4)+1)*√2/2
=(√2/(2+√2)+1)*√2/2
=1
f(x)求导得到
f'(π/4)
=-f'(π/4)*sin(π/4)+cos(π/4)
=-f'(π/4)*√2/2+√2/2
(1+√2/2)f'(π/4)=√2/2
f'(π/4)=√2/2/(1+√2/2)=√2/(2+√2)
f(π/4)
=f'(π/4)*cos(π/4)+sin(π/4)
=f'(π/4)*√2/2+√2/2
=(f'(π/4)+1)*√2/2
=(√2/(2+√2)+1)*√2/2
=1
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