derivative f(x)=(4x-7)/(28x^5)

Lösung

ableitung von

f (x) = \frac{4 x - 7}{28 x ^{5}}

\frac{- 16 x + 35}{28 x ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x - 7}{28 x ^{5}})

Entferne die Konstante:

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

= \frac{1}{28} \frac{d}{d x} (\frac{4 x - 7}{x ^{5}})

Wende die Quotientenregel an:

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

= \frac{1}{28} \cdot \frac{\frac{d}{d x} ( 4 x - 7 ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ( 4 x - 7 )}{( x ^{5} ) ^{2}}

\frac{d}{d x} (4 x - 7) = 4

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{1}{28} \cdot \frac{4 x ^{5} - 5 x ^{4} ( 4 x - 7 )}{( x ^{5} ) ^{2}}

Vereinfache

\frac{1}{28} \cdot \frac{4 x ^{5} - 5 x ^{4} ( 4 x - 7 )}{( x ^{5} ) ^{2}} : \frac{- 16 x + 35}{28 x ^{6}}

= \frac{- 16 x + 35}{28 x ^{6}}

\int_{0}^{\infty} \frac{1}{x ^{3}} d x

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

\int e^{s i n (t)} d t

\int \frac{36 - x ^{2}}{x} d x

y^{^{''}} = 36 x^{7} + 21 x^{5} - 3 x + 48 x^{- 5}