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Beliebt Rechnen >

implicit x=sec(1/y)

Lösung

implizite ableitung

x = sec (\frac{1}{y})

Lösung

\frac{d y}{d x} = - \frac{y ^{2}}{sec ( \frac{1}{y} ) tan ( \frac{1}{y} )}

Schritte zur Lösung

x = sec (\frac{1}{y})

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

1 = - \frac{sec ( \frac{1}{y} ) tan ( \frac{1}{y} ) \frac{d y}{d x}}{y ^{2}}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y ^{2}}{sec ( \frac{1}{y} ) tan ( \frac{1}{y} )}

\frac{d y}{d x} = - \frac{y ^{2}}{sec ( \frac{1}{y} ) tan ( \frac{1}{y} )}

Beliebte Beispiele

integral of 1/(y^2sqrt(14-y^2))

\int \frac{1}{y ^{2} 14 - y ^{2}} d y

6(dy)/(dx)+42y=7

6 \frac{d y}{d x} + 42 y = 7

derivative 1/4 (70x^2-8x^3)

d er i v a t i v e \frac{1}{4} (70 x^{2} - 8 x^{3})

limit as x approaches-3 of (x+2)/(x^2-9)

x \to - 3 lim (\frac{x + 2}{x ^{2} - 9})

derivative sqrt((z+1)/(z-1))

d er i v a t i v e \frac{z + 1}{z - 1}