derivative ((x^2+3)/(x^2-3))^3

Lösung

ableitung von

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

- \frac{36 x ( x ^{2} + 3 ) ^{2}}{( x ^{2} - 3 ) ^{4}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3}) = - \frac{12 x}{( x ^{2} - 3 ) ^{2}}

= 3 (\frac{x ^{2} + 3}{x ^{2} - 3})^{2} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}})

Vereinfache

3 (\frac{x ^{2} + 3}{x ^{2} - 3})^{2} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{36 x ( x ^{2} + 3 ) ^{2}}{( x ^{2} - 3 ) ^{4}}

= - \frac{36 x ( x ^{2} + 3 ) ^{2}}{( x ^{2} - 3 ) ^{4}}

\frac{\partial}{\partial x} (x \cdot e^{x y})

a re a x = y^{2} - 1, x = y

\frac{d}{d x} (2 x + x^{2})

(sin (t))^{^{'}}

d er i v a t i v e f (x) = 4 x^{2} - 15