Expression 11: StartFraction, 3 "x" squared times 5ln "x" minus "x" cubed times StartNestedFraction, 5 NestedOver "x" , EndNestedFraction Over left parenthesis, 5ln "x" , right parenthesis squared , EndFraction3x2·5lnx−x3·5x5lnx2
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Expression 12: StartFraction, 5 "x" squared left parenthesis, 3ln "x" minus StartNestedFraction, "x" NestedOver "x" , EndNestedFraction , right parenthesis Over 25ln squared "x" , EndFraction5x23lnx−xx25ln2x
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Expression 13: StartFraction, "x" squared left parenthesis, 3ln "x" minus 1 , right parenthesis Over 5ln squared "x" , EndFractionx23lnx−15ln2x
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Differentialkvotienten i x₀
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Expression 15: StartFraction, left parenthesis, StartNestedFraction, "d" NestedOver "d" "x" Subscript, 0 , Baseline , EndNestedFraction "f" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis , right parenthesis times "g" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis minus "f" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis times left parenthesis, StartNestedFraction, "d" NestedOver "d" "x" Subscript, 0 , Baseline , EndNestedFraction "g" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis , right parenthesis Over "g" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis squared , EndFractionddx0fx0·gx0−fx0·ddx0gx0gx02
equals=
0.5 7 0 4 9 5 6 4 2 5 4 20.570495642542
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Expression 16: StartFraction, "x" squared left parenthesis, 3ln "x" Subscript, 0 , Baseline minus 1 , right parenthesis Over 5ln squared "x" Subscript, 0 , Baseline , EndFractionx203lnx0−15ln2x0
equals=
0.5 7 0 4 9 5 6 4 2 5 4 20.570495642542
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Expression 17: "h" prime left parenthesis, "x" Subscript, 0 , Baseline , right parenthesish′x0
equals=
0.5 7 0 4 9 5 6 4 2 5 4 20.570495642542
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Tangent
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Expression 19: "y" equals "h" prime left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis left parenthesis, "x" minus "x" Subscript, 0 , Baseline , right parenthesis plus "h" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesisy=h′x0x−x0+hx0
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Expression 20: left parenthesis, "x" Subscript, 0 , Baseline plus "t" , "h" left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis plus "h" prime left parenthesis, "x" Subscript, 0 , Baseline , right parenthesis "t" , right parenthesisx0+t,hx0+h′x0t
domain t Minimum: negative 1−1
less than or equal to "t" less than or equal to≤t≤
domain t Maximum: 11
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Punkt
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"h" prime ( "x" Subscript, 0 , Baseline ) equals 0.5 7h′(x0)=0.57