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Beliebt Rechnen >

implicit (dy)/(dx),y^5=x^3

Lösung

implizite ableitung

\frac{d y}{d x}, y^{5} = x^{3}

Lösung

\frac{d y}{d x} = \frac{3 x ^{2}}{5 y ^{4}}

Schritte zur Lösung

y^{5} = x^{3}

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

5 y^{4} \frac{d y}{d x} = 3 x^{2}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{3 x ^{2}}{5 y ^{4}}

\frac{d y}{d x} = \frac{3 x ^{2}}{5 y ^{4}}

Beliebte Beispiele

integral of 5sec^2(1+5x)

\int 5 sec^{2} (1 + 5 x) d x

1/(x^8)(dy)/(dx)=12+15y

\frac{1}{x ^{8}} \frac{d y}{d x} = 12 + 15 y

derivative 5/(ln(x))

d er i v a t i v e \frac{5}{ln ( x )}

derivative of 1/(x-2-3)

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

limit as t approaches 1 of cos(pit)

t \to 1 lim (cos (π t))