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Beliebt Rechnen >

d/(dy)(x^{6y})

Lösung

\frac{d}{d y} (x^{6 y})

Lösung

6 x^{6 y} ln (x)

Schritte zur Lösung

\frac{d}{d y} (x^{6 y})

Behandle

x

als Konstante

Wende Exponentenregel an:

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

x^{6 y} = e^{6 y l n (x)}

= \frac{d}{d y} (e^{6 y l n (x)})

Wende die Kettenregel an:

e^{6 y l n (x)} \frac{d}{d y} (6 y ln (x))

= e^{6 y l n (x)} \frac{d}{d y} (6 y ln (x))

\frac{d}{d y} (6 y ln (x)) = 6 ln (x)

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

e^{6 y l n (x)} = x^{6 y}

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

Beliebte Beispiele

limit as x approaches-3 of (x+3)/(x-3)

x \to - 3 lim (\frac{x + 3}{x - 3})

derivative of (2x+1^4)

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

fläche y=3-x,y=(x^2)/4 ,x=2,x=1

a re a y = 3 - x, y = \frac{x ^{2}}{4}, x = 2, x = 1

3y^{''}+2y=5e^{2x}+2x^3

3 y^{^{''}} + 2 y = 5 e^{2 x} + 2 x^{3}

integral of 3/(2x^2)

\int \frac{3}{2 x ^{2}} d x