(\partial)/(\partial x)(y^{x^7})

Lösung

\frac{\partial}{\partial x} (y^{x^{7}})

7 x^{6} y^{x^{7}} ln (y)

Schritte zur Lösung

\frac{\partial}{\partial x} (y^{x^{7}})

Behandle

y

als Konstante

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

y^{x^{7}} = e^{x^{7} l n (y)}

= \frac{\partial}{\partial x} (e^{x^{7} l n (y)})

Wende die Kettenregel an:

e^{x^{7} l n (y)} \frac{\partial}{\partial x} (x^{7} ln (y))

= e^{x^{7} l n (y)} \frac{\partial}{\partial x} (x^{7} ln (y))

\frac{\partial}{\partial x} (x^{7} ln (y)) = 7 x^{6} ln (y)

= e^{x^{7} l n (y)} \cdot 7 x^{6} ln (y)

e^{x^{7} l n (y)} = y^{x^{7}}

= 7 x^{6} y^{x^{7}} ln (y)

x \to + 2 lim (\frac{x ^{2} - 4}{x - 2})

a re a x^{2}, 4 x

a re a y = 1 + 2 x, y = \frac{3 + x}{3}

a re a x, \frac{x}{2}

a re a y = \frac{1}{x}, y = \frac{1}{x ^{2}}, x = 4