Question

Найдите значение производной функции в заданной точке:
y=sin(x/3+п/4) x0=п/4 п-это пи

Answer 1

$y=sin(\frac{x}{3}+\frac{\pi}{4})\\\\y'=\frac{1}{3}\cdot cos(\frac{x}{3}+\frac{\pi}{4})\\\\y'(\frac{\pi}{4})=\frac{1}{3}\cdot cos(\frac{\pi}{12}+\frac{\pi}{4})=\frac{1}{3}\cdot cos\frac{\pi}{3}=\frac{1}{3}\cdot \frac{1}{2}=\frac{1}{6}$

Answer 2

Найдите значение производной функции f(x) =sin(x/3+π/4)   в  точке

x₀= π/4.

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f '(x) = ( sin(x/3+π/4) )' = cos(x/3+π/4) *( x/3+π/4 ) ' =

cos(x/3+π/4) *( (x/3) ' + (π/4 ) ' ) =cos(x/3+π/4) *( (1/3)*(x) ' + 0 )=

= (1/3)*cos(x/3+π/4) .

f '(x₀) = f '(π/4₀ ) = (1/3)*cos( (π/4)/3+π/4) = (1/3)*cos(π/3) =(1/3)*(1/2) =1/6 .