implicit (dy)/(dx),y^5=x^8

Lösung

implizite ableitung

\frac{d y}{d x}, y^{5} = x^{8}

\frac{d y}{d x} = \frac{8 x ^{7}}{5 y ^{4}}

Schritte zur Lösung

y^{5} = x^{8}

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

5 y^{4} \frac{d y}{d x} = 8 x^{7}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{8 x ^{7}}{5 y ^{4}}

\frac{d y}{d x} = \frac{8 x ^{7}}{5 y ^{4}}

\int x (5^{- x^{2}}) d x

\int 1 - x d x

\int (3 x^{4} - 4 x^{3} + 6 x^{2} - \frac{x}{2} + 3) d x

\int 8 tan (x) sin (y) cos (y) d x

\frac{d}{d x} ((2 x^{2} - 7)^{5} - (1 + 4 x^{3})^{5})