tangent ((x^4+1))/(e^x+2x+1)

Lösung

tangente von

\frac{( x ^{4} + 1 )}{e ^{x} + 2 x + 1}

y = \frac{6 a _{0}^{4} - e ^{a_{0}} a _{0}^{4} + 4 e ^{a_{0}} a _{0}^{3} + 4 a _{0}^{3} - e ^{a_{0}} - 2}{( e ^{a_{0}} + 2 a _{0} + 1 ) ^{2}} x + \frac{- 4 a _{0}^{5} + a _{0}^{5} e ^{a_{0}} - 3 a _{0}^{4} e ^{a_{0}} - 3 a _{0}^{4} + 4 a _{0} + a _{0} e ^{a_{0}} + e ^{a_{0}} + 1}{( 2 a _{0} + e ^{a_{0}} + 1 ) ^{2}}

Schritte zur Lösung

Berechne den Graphen der Tangente für den allgemeinen Punkt

x = a_{0}

Finde den Tangentenpunkt:

(a_{0}, \frac{a _{0}^{4} + 1}{e ^{a_{0}} + 2 a _{0} + 1})

Finde die Steigung von

y = \frac{x ^{4} + 1}{e ^{x} + 2 x + 1} : \frac{d y}{d x} = \frac{6 x ^{4} - e ^{x} x ^{4} + 4 e ^{x} x ^{3} + 4 x ^{3} - e ^{x} - 2}{( e ^{x} + 2 x + 1 ) ^{2}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{6 a _{0}^{4} - e ^{a_{0}} a _{0}^{4} + 4 e ^{a_{0}} a _{0}^{3} + 4 a _{0}^{3} - e ^{a_{0}} - 2}{( e ^{a_{0}} + 2 a _{0} + 1 ) ^{2}}

Finde den Graphen mit Steigung m=

\frac{6 a _{0}^{4} - e ^{a_{0}} a _{0}^{4} + 4 e ^{a_{0}} a _{0}^{3} + 4 a _{0}^{3} - e ^{a_{0}} - 2}{( e ^{a_{0}} + 2 a _{0} + 1 ) ^{2}}

, der durch den Punkt

(a_{0}, \frac{a _{0}^{4} + 1}{e ^{a_{0}} + 2 a _{0} + 1})

verläuft:

y = \frac{6 a _{0}^{4} - e ^{a_{0}} a _{0}^{4} + 4 e ^{a_{0}} a _{0}^{3} + 4 a _{0}^{3} - e ^{a_{0}} - 2}{( e ^{a_{0}} + 2 a _{0} + 1 ) ^{2}} x + \frac{- 4 a _{0}^{5} + a _{0}^{5} e ^{a_{0}} - 3 a _{0}^{4} e ^{a_{0}} - 3 a _{0}^{4} + 4 a _{0} + a _{0} e ^{a_{0}} + e ^{a_{0}} + 1}{( 2 a _{0} + e ^{a_{0}} + 1 ) ^{2}}

y = \frac{6 a _{0}^{4} - e ^{a_{0}} a _{0}^{4} + 4 e ^{a_{0}} a _{0}^{3} + 4 a _{0}^{3} - e ^{a_{0}} - 2}{( e ^{a_{0}} + 2 a _{0} + 1 ) ^{2}} x + \frac{- 4 a _{0}^{5} + a _{0}^{5} e ^{a_{0}} - 3 a _{0}^{4} e ^{a_{0}} - 3 a _{0}^{4} + 4 a _{0} + a _{0} e ^{a_{0}} + e ^{a_{0}} + 1}{( 2 a _{0} + e ^{a_{0}} + 1 ) ^{2}}

d er i v a t i v e 12 x^{3} - 24 x^{2}

f (I) = I^{22}

\int \frac{x ^{2} + 8}{x ^{4} - x ^{3} - 2 x ^{2}} d x

x \to + x lim (\frac{x ^{2} - 1}{x - 1})

d er i v a t i v e f (x) = \frac{7}{( x ^{2} - 10 ) ^{4}}