(\partial)/(\partial y)(x^{y-1})

Lösung

\frac{\partial}{\partial y} (x^{y - 1})

x^{y - 1} ln (x)

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{y - 1})

Behandle

x

als Konstante

Wende Exponentenregel an:

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

x^{y - 1} = e^{(y - 1) l n (x)}

= \frac{\partial}{\partial y} (e^{(y - 1) l n (x)})

Wende die Kettenregel an:

e^{(y - 1) l n (x)} \frac{\partial}{\partial y} ((y - 1) ln (x))

= e^{(y - 1) l n (x)} \frac{\partial}{\partial y} ((y - 1) ln (x))

\frac{\partial}{\partial y} ((y - 1) ln (x)) = ln (x)

= e^{(y - 1) l n (x)} ln (x)

e^{(y - 1) l n (x)} = x^{y - 1}

= x^{y - 1} ln (x)

x (\frac{d y}{d x}) + 2 y = 3

\frac{\partial}{\partial y} (\frac{2}{y})

d er i v a t i v e f (x) = 2 sec (x) tan (x)

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

f (x) = e^{x} + ln (x + 1)