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9856565651
@9856565651
July 2022
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oganesbagoyan
Verified answer
1)
f '(x) =(4x³ +6x+3)' = 4(x³) ' +6*(x)' +3 ' =4*3x² +6 =6(2x² +1) .
f '(x(0)) = f '(1)=6(2*1² +1) =6*3 =18.
4)
f '(x) =
(
(√x+1)/√x)
)
' =(1+1/√x)' =1' +
(
x) ^(-1/2)
)
' =0 - 1/2*(x) ^(-3/2) = -1/(2x√x) .
f '(x(0)) = f '(1) = -1/(2*1*√1)
= -0,5
.
или
f '(x) =
(
(√x+1)/√x)
)
' =
(
(√x+1)' *√x -(√x+1)*(√x)'
)/(
√x
)
² =
(
1/(2√x) *√x -(√x+1)*1/((2√x)
)/
x =
(
1/(2√x) *(√x - √x-1) /x = -1/(2x√x).
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Answers & Comments
Verified answer
1) f '(x) =(4x³ +6x+3)' = 4(x³) ' +6*(x)' +3 ' =4*3x² +6 =6(2x² +1) .f '(x(0)) = f '(1)=6(2*1² +1) =6*3 =18.
4) f '(x) =((√x+1)/√x)) ' =(1+1/√x)' =1' +( x) ^(-1/2)) ' =0 - 1/2*(x) ^(-3/2) = -1/(2x√x) .
f '(x(0)) = f '(1) = -1/(2*1*√1) = -0,5.
или
f '(x) =((√x+1)/√x)) ' = ( (√x+1)' *√x -(√x+1)*(√x)' )/(√x)² =( 1/(2√x) *√x -(√x+1)*1/((2√x) )/ x =( 1/(2√x) *(√x - √x-1) /x = -1/(2x√x).