derivative of x/(sqrt(x^2+36))

Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 36})

\frac{36}{( x ^{2} + 36 ) x ^{2} + 36}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 36})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{2} + 36) = \frac{x}{x ^{2} + 36}

= \frac{1 \cdot x ^{2} + 36 - \frac{x}{x ^{2} + 36} x}{( x ^{2} + 36 ) ^{2}}

Vereinfache

\frac{1 \cdot x ^{2} + 36 - \frac{x}{x ^{2} + 36} x}{( x ^{2} + 36 ) ^{2}} : \frac{36}{( x ^{2} + 36 ) x ^{2} + 36}

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

\frac{\partial}{\partial x} (x^{3} - 3 x y)

\int_{0}^{7} \frac{8}{9 x ^{2} + 10 x + 1} d x

\int \frac{1}{x ^{2} x ^{2} - 100} d x

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

x \to 3 lim (5^{x})