derivative (1+5t)/(ln(t^2))

Lösung

ableitung von

\frac{1 + 5 t}{ln ( t ^{2} )}

\frac{5 t ln ( t ^{2} ) - 2 ( 1 + 5 t )}{t ln ^{2} ( t ^{2} )}

Schritte zur Lösung

\frac{d}{d t} (\frac{1 + 5 t}{ln ( t ^{2} )})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d t} ( 1 + 5 t ) ln ( t ^{2} ) - \frac{d}{d t} ( ln ( t ^{2} ) ) ( 1 + 5 t )}{( ln ( t ^{2} ) ) ^{2}}

\frac{d}{d t} (1 + 5 t) = 5

\frac{d}{d t} (ln (t^{2})) = \frac{2}{t}

= \frac{5 ln ( t ^{2} ) - \frac{2}{t} ( 1 + 5 t )}{( ln ( t ^{2} ) ) ^{2}}

Vereinfache

\frac{5 ln ( t ^{2} ) - \frac{2}{t} ( 1 + 5 t )}{ln ^{2} ( t ^{2} )} : \frac{5 t ln ( t ^{2} ) - 2 ( 1 + 5 t )}{t ln ^{2} ( t ^{2} )}

= \frac{5 t ln ( t ^{2} ) - 2 ( 1 + 5 t )}{t ln ^{2} ( t ^{2} )}

\int \frac{x ^{2}}{x ^{6} - 1} d x

\int_{1}^{10} 5 x^{- 2} d x

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\frac{\partial}{\partial y} (7 x sin (9 x^{2} y))