已知f（x）=lnx+cosx，则f（x）在x＝π2处的导数值为2π−12π−1．

Question

已知f（x）=lnx+cosx，则f（x）在x＝(π)/(2)处的导数值为

(2)/(π)−1

(2)/(π)−1

．

Answer 1

∵f（x）=lnx+cosx，
∴f′（x）=(1)/(x)−sinx，
∴f（x）在x＝(π)/(2)处的导数值为f′（(π)/(2)）=(1)/((π)/(2))−sin(π)/(2)=(2)/(π)−1，
∴f（x）在x＝(π)/(2)处的导数值为(2)/(π)−1．
故答案为：(2)/(π)−1．