·已知函数f(x)= f

2020-12-30社会538

注意到等式中f'(pi/4)是常数,所以

f'(x)=f'(pi/4)(-sinx)+cosx

--->f'(pi/4)=f'(pi/4)[-sin(pi/4)]+cos(pi/4)]

--->f'(pi/4)=f'(pi/4)(-√2/2)+√2/2

--->f'(pi/4)(1+√2/2)=√2/2

--->f'(pi/4)=(√2/2)/(1+√2/2)=1/(√2+1)=√2-1.

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