derivative of (5x/((x^2+1)^{3/5)})

Lösung

\frac{d}{d x} (\frac{5 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

\frac{- x ^{2} + 5}{( x ^{2} + 1 ) ^{\frac{8}{5}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (\frac{x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} ((x^{2} + 1)^{\frac{3}{5}}) = \frac{6 x}{5 ( x ^{2} + 1 ) ^{\frac{2}{5}}}

= 5 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{\frac{3}{5}} - \frac{6 x}{5 ( x ^{2} + 1 ) ^{\frac{2}{5}}} x}{( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) ^{2}}

Vereinfache

5 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{\frac{3}{5}} - \frac{6 x}{5 ( x ^{2} + 1 ) ^{\frac{2}{5}}} x}{( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) ^{2}} : \frac{- x ^{2} + 5}{( x ^{2} + 1 ) ^{\frac{8}{5}}}

= \frac{- x ^{2} + 5}{( x ^{2} + 1 ) ^{\frac{8}{5}}}

\frac{\partial}{\partial x} (sin (4 x + 4 y))

\frac{d}{d x} ((1 - x^{2})^{5})

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

\int \frac{- y}{1 + y ^{2}} d y

\int_{0}^{2} \frac{1}{4 - x ^{2}} d x