implicit (dy)/(dx),x^2+xy+y^2=7

Lösung

implizite ableitung

\frac{d y}{d x}, x^{2} + x y + y^{2} = 7

\frac{d y}{d x} = \frac{- 2 x - y}{x + 2 y}

Schritte zur Lösung

x^{2} + x y + y^{2} = 7

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

2 x + y + x \frac{d y}{d x} + 2 y \frac{d y}{d x} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 2 x - y}{x + 2 y}

\frac{d y}{d x} = \frac{- 2 x - y}{x + 2 y}

\int_{0}^{\frac{π}{3}} 2 sec^{2} (x) d x

a re a f (x) = x + 3, g (x) = \frac{1}{2} x + 3

\int_{0}^{5} \frac{1}{( 5 - x ) ^{\frac{1}{3}}} d x

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

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