derivative of (7x^2/(x^3))

Lösung

\frac{d}{d x} (\frac{7 x ^{2}}{x ^{3}})

- \frac{7}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x ^{2}}{x ^{3}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (\frac{x ^{2}}{x ^{3}})

Wende die Quotientenregel an:

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

= 7 \cdot \frac{\frac{d}{d x} ( x ^{2} ) x ^{3} - \frac{d}{d x} ( x ^{3} ) x ^{2}}{( x ^{3} ) ^{2}}

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

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

= 7 \cdot \frac{2 x x ^{3} - 3 x ^{2} x ^{2}}{( x ^{3} ) ^{2}}

Vereinfache

7 \cdot \frac{2 x x ^{3} - 3 x ^{2} x ^{2}}{( x ^{3} ) ^{2}} : - \frac{7}{x ^{2}}

= - \frac{7}{x ^{2}}

x \to 0 lim ((1 + x)^{\frac{7}{x}})

k (\frac{d x}{d t}) = x + 15

\int_{0}^{10} x d x

\frac{d}{d x} (\frac{( x ^{2} + 1 ) ^{2}}{( x ^{4} + 1 ) ^{4}})

x \to 2 lim (\frac{2 x - 8}{x - 1})