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inkognitous
@inkognitous
September 2021
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Помогите с производными - 50 баллов
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oganesbagoyan
Verified answer
F(x) =2/x⁷ ;
f '(x) =(2x^(-7))' = 2* (-7)*x ^(-7 -1) = -14x^(-8)
=
-14/x
⁸
.
---------
y = x⁴/4 ;x(0) = -1.
----
α =(T^X+) - ?
tqα = y'(x(0)) ;
y' = (x⁴/4) =4x³/4 =x³ ;
y'(x(0)) = (-1)³ = -1 .
tqα = -1 ⇒
α = 135°.
---------
а)
f(x) =(x² -3)/x ;
---
f'(x(0)) =
f'(2) - ?
производная дроби :
f'(x) =((x² -3)/x) =
(
(x² -3)' *x -(x² -3)*(x)'
)/
x² =(2x² - x²+3)/x² =1+3/x².
или по другому
f(x) =x -3*x ^(-1)⇒ f'(x) = (x -3*x ^(-1))' = 1 - 3*(-1)*x ^(-1-1) = 1 + 3/x² .
f'(2)
=1+ 3/2²
=1,75
.
---------
б)
f(x) =xcosx ;
---
f'(x(0)) =
f'(π) - ?
производная произведения :
f'(x) = (xcosx) = (x)'*cosx + x*(cosx) ' =cosx + x*(-sinx) =cosx -xsinx.
f'(π)
= cosπ -πsinπ = -1 -π*0 =
-1.
Думаю все .
УДАЧИ !
2 votes
Thanks 1
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Answers & Comments
Verified answer
F(x) =2/x⁷ ;f '(x) =(2x^(-7))' = 2* (-7)*x ^(-7 -1) = -14x^(-8) =-14/x⁸ .
---------
y = x⁴/4 ;x(0) = -1.
----
α =(T^X+) - ?
tqα = y'(x(0)) ;
y' = (x⁴/4) =4x³/4 =x³ ;
y'(x(0)) = (-1)³ = -1 .
tqα = -1 ⇒ α = 135°.
---------
а) f(x) =(x² -3)/x ;
---
f'(x(0)) = f'(2) - ?
производная дроби :
f'(x) =((x² -3)/x) = ((x² -3)' *x -(x² -3)*(x)' )/ x² =(2x² - x²+3)/x² =1+3/x².
или по другому
f(x) =x -3*x ^(-1)⇒ f'(x) = (x -3*x ^(-1))' = 1 - 3*(-1)*x ^(-1-1) = 1 + 3/x² .
f'(2) =1+ 3/2² =1,75 .
---------
б) f(x) =xcosx ;
---
f'(x(0)) = f'(π) - ?
производная произведения :
f'(x) = (xcosx) = (x)'*cosx + x*(cosx) ' =cosx + x*(-sinx) =cosx -xsinx.
f'(π) = cosπ -πsinπ = -1 -π*0 = -1.
Думаю все .
УДАЧИ !