关于问题1至8中的x的微分函数
问题1.罪(x 2 + 5)
解决方案:
y = sin(x2 + 5)
=
= cos(x2 + 5) ×
= cos(x2 + 5) × (2x)
dy/dx = 2xcos(x2 + 5)
问题2. cos(sin x)
解决方案:
y = cos(sin x)
=
= -sin(sin x) ×
= -sin(sin x)cos x
问题3. sin(ax + b)
解决方案:
y = sin(ax + b)
= a cos(ax + b)
问题4.秒(tan(√x)
解决方案:
y = sec(tan√x)
=
= sec(tan √x) × tan(√x) ×
= sec (tan √x) × tan (tan √x) × sec2√x ×
= sec(tan√x)tan(tan√x)(sec2√x)1/(2√x)
= 1/(2√x) × sec(tan√x)tan(tan√x)(sec2√x)
问题5
解决方案:
y =
=
问题6. cos x 3 .sin 2 (x 5 )
解决方案:
y = cos x3.sin2(x5)
=
= cos x3.2sin(x5) .cos(x5(5x4)(5x4) – sin2(x5).sin x3.3x2
= 10x4 cos x3sin(x5)cos(x5) – 3x2 sin2(x5)sin x3
问题7.2√(cos(x 2 ))
解决方案:
y = 2√(cos(x2))
=
= 2
=
=
=
=
=
=
=
=
=
=
=
问题8. cos(√x)
解决方案:
y = cos (√x)
dy/dx = -sin√x
=
=
问题9.证明由f(x)= | x – 1 |,x∈R给出的函数f在x = 1时不可微。
解决方案:
=
=
=
= +1
=
=
=
= -1
LHD ≠ RHD
Hence, f(x) is not differentiable at x = 1
问题10.证明由f(x)= [x],0
解决方案:
Given: f(x) = [x], 0 < x < 3
LHS:
f'(1) =
=
=
= ∞
RHS:
f'(1) =
=
=
=
= 0
LHS ≠ RHS
So, the given f(x) = [x] is not differentiable at x = 1.
Similarly, the given f(x) = [x] is not differentiable at x = 2.
解决方案:
Given: f(x) = [x], 0 < x < 3
LHS:
f'(1) =
=
=
= ∞
RHS:
f'(1) =
=
=
=
= 0
LHS ≠ RHS
So, the given f(x) = [x] is not differentiable at x = 1.
Similarly, the given f(x) = [x] is not differentiable at x = 2.