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Beliebt Rechnen >

d/(dy)(x^{8y})

Lösung

\frac{d}{d y} (x^{8 y})

Lösung

8 x^{8 y} ln (x)

Schritte zur Lösung

\frac{d}{d y} (x^{8 y})

Behandle

x

als Konstante

Wende Exponentenregel an:

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

x^{8 y} = e^{8 y l n (x)}

= \frac{d}{d y} (e^{8 y l n (x)})

Wende die Kettenregel an:

e^{8 y l n (x)} \frac{d}{d y} (8 y ln (x))

= e^{8 y l n (x)} \frac{d}{d y} (8 y ln (x))

\frac{d}{d y} (8 y ln (x)) = 8 ln (x)

= e^{8 y l n (x)} \cdot 8 ln (x)

e^{8 y l n (x)} = x^{8 y}

= 8 x^{8 y} ln (x)

Beliebte Beispiele

integral of 2pixsin(x^2)

\int 2 π x sin (x^{2}) d x

implicit (dy)/(dx),x^{1/2}+y^{1/2}=9

im pl i c i t \frac{d y}{d x}, x^{\frac{1}{2}} + y^{\frac{1}{2}} = 9

integral of (arcsin^3(x))/(sqrt(1-x^2))

\int \frac{arcsin ^{3} ( x )}{1 - x ^{2}} d x

integral of t^2+1

\int t^{2} + 1 d t

derivative of sqrt(x-2y)

\frac{d}{d x} (x - 2 y)