derivative (c^4-x^4)/(c^4+x^4)

Lösung

ableitung von

\frac{c ^{4} - x ^{4}}{c ^{4} + x ^{4}}

- \frac{8 c ^{4} x ^{3}}{( c ^{4} + x ^{4} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{c ^{4} - x ^{4}}{c ^{4} + x ^{4}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( c ^{4} - x ^{4} ) ( c ^{4} + x ^{4} ) - \frac{d}{d x} ( c ^{4} + x ^{4} ) ( c ^{4} - x ^{4} )}{( c ^{4} + x ^{4} ) ^{2}}

\frac{d}{d x} (c^{4} - x^{4}) = - 4 x^{3}

\frac{d}{d x} (c^{4} + x^{4}) = 4 x^{3}

= \frac{( - 4 x ^{3} ) ( c ^{4} + x ^{4} ) - 4 x ^{3} ( c ^{4} - x ^{4} )}{( c ^{4} + x ^{4} ) ^{2}}

Vereinfache

\frac{( - 4 x ^{3} ) ( c ^{4} + x ^{4} ) - 4 x ^{3} ( c ^{4} - x ^{4} )}{( c ^{4} + x ^{4} ) ^{2}} : - \frac{8 c ^{4} x ^{3}}{( c ^{4} + x ^{4} ) ^{2}}

= - \frac{8 c ^{4} x ^{3}}{( c ^{4} + x ^{4} ) ^{2}}

\int sin (x^{3}) x^{2} d x

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

x \to 0 - lim (\frac{x - 1}{x ^{2}})

f (t) = sin (t^{2})

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