implicit x^5+y^5=10

Lösung

implizite ableitung

x^{5} + y^{5} = 10

\frac{d y}{d x} = - \frac{x ^{4}}{y ^{4}}

Schritte zur Lösung

x^{5} + y^{5} = 10

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

5 x^{4} + 5 y^{4} \frac{d y}{d x} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{x ^{4}}{y ^{4}}

\frac{d y}{d x} = - \frac{x ^{4}}{y ^{4}}

x \to 0 - lim (\frac{1}{13 x})

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

\int t e^{- t^{2}} d t

x \to - \frac{π}{9} lim (9 x^{2} (5 x))

\int cot^{6} (x) csc^{2} (x) d x