derivative of sqrt((x^2-4(y^2-9)))

Lösung

\frac{d}{d x} ((x^{2} - 4) (y^{2} - 9))

\frac{x ( y ^{2} - 9 ) + y \frac{d y}{d x} ( x ^{2} - 4 )}{( x ^{2} - 4 ) ( y ^{2} - 9 )}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 4) (y^{2} - 9))

Wende die Kettenregel an:

\frac{1}{2 ( x ^{2} - 4 ) ( y ^{2} - 9 )} \frac{d}{d x} ((x^{2} - 4) (y^{2} - 9))

= \frac{1}{2 ( x ^{2} - 4 ) ( y ^{2} - 9 )} \frac{d}{d x} ((x^{2} - 4) (y^{2} - 9))

\frac{d}{d x} ((x^{2} - 4) (y^{2} - 9)) = 2 x (y^{2} - 9) + 2 y \frac{d y}{d x} (x^{2} - 4)

= \frac{1}{2 ( x ^{2} - 4 ) ( y ^{2} - 9 )} (2 x (y^{2} - 9) + 2 y \frac{d y}{d x} (x^{2} - 4))

Vereinfache

\frac{1}{2 ( x ^{2} - 4 ) ( y ^{2} - 9 )} (2 x (y^{2} - 9) + 2 y \frac{d y}{d x} (x^{2} - 4)) : \frac{x ( y ^{2} - 9 ) + y \frac{d y}{d x} ( x ^{2} - 4 )}{( x ^{2} - 4 ) ( y ^{2} - 9 )}

= \frac{x ( y ^{2} - 9 ) + y \frac{d y}{d x} ( x ^{2} - 4 )}{( x ^{2} - 4 ) ( y ^{2} - 9 )}

e x t re m e 9 x^{8} + 1

e x t re m e f (x) = e

e x t re m e f (x, y) = 3 x^{2} - 9 y^{2} - 24 x - 54 y + 2

e x t re m e f (x) = - \frac{e ^{2 x}}{- 2 x - 5}

e x t re m e f (x) = (10 - 2 x) (10 - 2 x) (x)