tangent f(x)=(2x+4)^{1/5},\at x=1

Lösung

tangente von

f (x) = (2 x + 4)^{\frac{1}{5}}, at x = 1

y = \frac{2 ^{\frac{1}{5}}}{5 \cdot 3 ^{\frac{4}{5}}} x + 6^{\frac{1}{5}} - \frac{2 ^{\frac{1}{5}}}{5 \cdot 3 ^{\frac{4}{5}}}

Schritte zur Lösung

Finde den Tangentenpunkt:

(1, 6^{\frac{1}{5}})

Finde die Steigung von

f (x) = (2 x + 4)^{\frac{1}{5}} : \frac{df ( x )}{d x} = \frac{2}{5 ( 2 x + 4 ) ^{\frac{4}{5}}}

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{2 ^{\frac{1}{5}}}{5 \cdot 3 ^{\frac{4}{5}}}

Finde den Graphen mit Steigung m=

\frac{2 ^{\frac{1}{5}}}{5 \cdot 3 ^{\frac{4}{5}}}

, der durch den Punkt

(1, 6^{\frac{1}{5}})

verläuft:

y = \frac{2 ^{\frac{1}{5}}}{5 \cdot 3 ^{\frac{4}{5}}} x + 6^{\frac{1}{5}} - \frac{2 ^{\frac{1}{5}}}{5 \cdot 3 ^{\frac{4}{5}}}

y = \frac{2 ^{\frac{1}{5}}}{5 \cdot 3 ^{\frac{4}{5}}} x + 6^{\frac{1}{5}} - \frac{2 ^{\frac{1}{5}}}{5 \cdot 3 ^{\frac{4}{5}}}

y \to \infty lim (\frac{( y ^{2} - e ^{(6 y)} )}{( 4 y ^{2} + e ^{7 y} )})

d er i v a t i v e h (t) = (t + 1)^{\frac{2}{3}} (2 t^{2} - 1)^{3}

\frac{\partial}{\partial y} (4 x^{3} y^{3} + 1)

\int \frac{1}{5 x + 6} d x

\int \frac{3 x + 6}{( 2 x ^{2} + 8 x + 3 ) ^{2}} d x