F. 5 - A.Maths - 微分法 - 鏈式法則

g(t) solution is wrong, the above person missed the (4t[^2]) for differentiation!!


f'(x) = 65??


it should be -81 instead, please check your calculation!!


f(x) = 3x(2x+5)^7

f'(x) = 3(2x+5)^7 + 3x(7)(2x+5)^6(2)

f'(x) = 3(2x+5)^7 + 42x(2x+5)^6

f'(x) = 3(2x+5)^6[2x+5+14x]

f'(x) = 3(2x+5)^6[16x+5]

f'(-2) = 3(2[-2]+5)^6[16(-2)+5]

f'(-2) = 3(-4+5)^6[-32+5]

f'(-2) = 3(1)^6[-27] = 3 x 1 x 1 x 1 x 1 x 1 x 1 x (-27) = -81!!

1)g(t) = (4t + 7)^2(2t^3 + 1)^4
g'(t)=[(4t + 7)^2](6t^2)[(2t^3 + 1)^3]+[(2t^3 + 1)^4][8t(4t + 7)]
=2t(4t + 7)[(2t^3 + 1)^3][3t(4t + 7)+4(2t^3 + 1)]
=2t(4t + 7)[(2t^3 + 1)^3](20t^3+21t+4)

2)H(z) = (2z + 5)^-1 (4z + 3 )^ -2
H'(z)= [(2z + 5)^-1](4)[(4z+3)^-3]+[(4z + 3 )^ -2](2)[(2z + 5)^-2]
=2[(2z + 5)^-2][(4z+3)^-3][2(2z+5)+(4z+3)]
=2[(2z + 5)^-2][(4z+3)^-3](8z+13)

3) f(x) = 3x(2x + 5)^7
f'(x)=3x(7)(2)(2x + 5)^6+3(2x + 5)^7
=42x(2x + 5)^6+3(2x + 5)^7
=3[(2x + 5)^6][14+(2x + 5)]
=3[(2x + 5)^6](2x+19)
f'(-2)=3[(2(-2) + 5)^6](2(-2)+19)
=65
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