derivative (t^5-3t^2)/(2t)

Lösung

ableitung von

\frac{t ^{5} - 3 t ^{2}}{2 t}

\frac{1}{2} (4 t^{3} - 3)

Schritte zur Lösung

\frac{d}{d t} (\frac{t ^{5} - 3 t ^{2}}{2 t})

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d t} (\frac{t ^{5} - 3 t ^{2}}{t})

Wende die Quotientenregel an:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d t} ( t ^{5} - 3 t ^{2} ) t - \frac{d t}{d t} ( t ^{5} - 3 t ^{2} )}{t ^{2}}

\frac{d}{d t} (t^{5} - 3 t^{2}) = 5 t^{4} - 6 t

\frac{d t}{d t} = 1

= \frac{1}{2} \cdot \frac{( 5 t ^{4} - 6 t ) t - 1 \cdot ( t ^{5} - 3 t ^{2} )}{t ^{2}}

\frac{( 5 t ^{4} - 6 t ) t - 1 \cdot ( t ^{5} - 3 t ^{2} )}{t ^{2}} = 4 t^{3} - 3

= \frac{1}{2} (4 t^{3} - 3)

\int \frac{x}{x + 5} d x

d er i v a t i v e f (x) = 7 e^{- x} - 4 e^{- 7 x}

\frac{\partial}{\partial x} (3 sec^{2} (3 x - 2 y + 1))

\frac{d}{d x} ((2 x + 3)^{5} + 10 x (2 x + 3)^{4})

21 x y^{^{'}} + y = 462 x