Вычислите значение производной функции
[tex]y = (4x - 10)^{4} [/tex]
в точке
[tex] x_{0} = 2[/tex]
[tex]y = (4x - 10)^{4} [/tex]
в точке
[tex] x_{0} = 2[/tex]
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Answers & Comments
Verified answer
((4x-10)²)²= (16x²-80x+100)(16x²-80x+100)= 256x^4-1280x³+1600x²-1280x³+6400x²-8000x+1600x²-8000x+10000= 256x^4-2560x³+9600x²-16000x+10000y'(x)= 1024x³-7680x²+19200x-16000= 128(8x³-60x²+150x-125)= 128(2x-5)³
y'(2)= 128*(2*2-5)³= 128*(-1)³= -128
Verified answer
Решение:1) у = (4х - 10)^ 4
у' = ((4х - 10)^ 4)' = 4•(4х - 10)^3• (4х - 10)' = 16• (4х - 10)^3.
2) Если х0 = 2, то
у' (х0)= у' (2)= 16• (4•2 - 10)^3.= 16•(- 8)= - 128.
Ответ: - 128.