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Beliebt Rechnen >

implicit (dy)/(dx),x^{(2/3)}+y^{(2/3)}=10

Lösung

implizite ableitung

\frac{d y}{d x}, x^{(\frac{2}{3})} + y^{(\frac{2}{3})} = 10

Lösung

\frac{d y}{d x} = - (\frac{y}{x})^{\frac{1}{3}}

Schritte zur Lösung

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 10

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

\frac{2}{3 x ^{\frac{1}{3}}} + \frac{2 \frac{d y}{d x}}{3 y ^{\frac{1}{3}}} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = - (\frac{y}{x})^{\frac{1}{3}}

\frac{d y}{d x} = - (\frac{y}{x})^{\frac{1}{3}}

Beliebte Beispiele

derivative Y(θ)=cot^2(cos(θ))

d er i v a t i v e Y (θ) = cot^{2} (cos (θ))

derivative f(t)=6t-5t^2

d er i v a t i v e f (t) = 6 t - 5 t^{2}

derivative of (x^3+6e^x)

\frac{d}{d x} ((x^{3} + 6) e^{x})

derivative of sinh(0)

\frac{d}{d x} (sinh (0))

(dv)/(dt)= 1/(t^2)

\frac{d v}{d t} = \frac{1}{t ^{2}}