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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{x}{3}

\int (- 4 x^{6} - 3 x^{5} + 5 e^{x}) d x

\frac{d}{d x} (x^{3} + 3 x^{2} - 6 x - 8)

\int \frac{( arctan ( x ) ) ^{7}}{x ^{2} + 1} d x

d er i v a t i v e f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 3)