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Beliebt Rechnen >

derivative of x^ay^{1-a}

Lösung

\frac{d}{d x} (x^{a} y^{1 - a})

Lösung

a x^{a - 1} y^{1 - a} + y^{- a} (1 - a) \frac{d y}{d x} x^{a}

Schritte zur Lösung

\frac{d}{d x} (x^{a} y^{1 - a})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{a}, g = y^{1 - a}

= \frac{d}{d x} (x^{a}) y^{1 - a} + \frac{d}{d x} (y^{1 - a}) x^{a}

\frac{d}{d x} (x^{a}) = a x^{a - 1}

\frac{d}{d x} (y^{1 - a}) = y^{- a} (1 - a) \frac{d y}{d x}

= a x^{a - 1} y^{1 - a} + y^{- a} (1 - a) \frac{d y}{d x} x^{a}

Beliebte Beispiele

steigung (1,-1),(6,-1)

s l o p e (1, - 1), (6, - 1)

integral from 6 to 8 of (92)/((x-6)^3)

\int_{6}^{8} \frac{92}{( x - 6 ) ^{3}} d x

derivative of sin^4(cos(8x))

\frac{d}{d x} (sin^{4} (cos (8 x)))

limit as x approaches 4 of x^4-5x^2+2

x \to 4 lim (x^{4} - 5 x^{2} + 2)

fläche f(x)= 1/x ,[1,2]

a re a f (x) = \frac{1}{x}, [1, 2]