implicit (dy)/(dx),16x^2-16xy+y^2=1

Lösung

implizite ableitung

\frac{d y}{d x}, 16 x^{2} - 16 x y + y^{2} = 1

\frac{d y}{d x} = \frac{8 ( y - 2 x )}{y - 8 x}

Schritte zur Lösung

16 x^{2} - 16 x y + y^{2} = 1

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

32 x - 16 (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{8 ( y - 2 x )}{y - 8 x}

\frac{d y}{d x} = \frac{8 ( y - 2 x )}{y - 8 x}

x \to 0 lim (x^{2} \cdot ln (x))

\int_{1}^{2} \frac{1}{x ^{2}} d x

x \to 0 + lim (x (ln (x)))

t an g e n t 4 x^{2} - 3 x + 2

f^{^{'}} (x) = 2 x + 3 x^{1.7}