Question

求以下三个函数的导数

书上答案貌似有错的

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Answer 1

第1题
arctanx(1-2x)² ′
= (1-2x)² ′/(1+(1-2x)⁴ )
= -4(1-2x)/(1+(1-2x)⁴ )
=4(2x-1)/(1+(2x-1)⁴ )

第2题
y ′
=(2^x√x²+1) ′sinx + (2^x√x²+1) cosx
=(㏑2‧2^x‧√x²+1 + 2^x‧x/√x²+1) sinx + (2^x√x²+1) cosx
=2^x sinx(㏑2(x²+1) + x)/(√x²+1)
+2^x√x² cosx
+cosx

第3题
f ′(x)=(sinx sin3x)′sin5x+5(sinx sin3x)cos5x
=(cosx sin3x+3sinx cos3x)sin5x+5sinx sin3x cos5x
=cosx sin3x sin5x+3sinx cos3x sin5x+5sinx sin3x cos5x

f''(x)=-sinx sin3x sin5x +cosx (sin3x sin5x) ′+
-9sinx sin3x sin5x + 3cos3x (sinx sin5x) ′+
-25sinx sin3x sin5x + 5(sinx sin3x ) ′cos5x

=-35sinx sin3x sin5x +
cosx (3cos3x sin5x + 5sin3x cos5x) +
3cos3x (cosx sin5x + 5sinx cos5x) +
5cos5x( cosx sin3x + 3sinx cos3x)

f''(0)=0

Answer 2