derivative f(z)=sqrt((z-4)/(z+4))

Lösung

ableitung von

f (z) = \frac{z - 4}{z + 4}

\frac{4}{z - 4 ( z + 4 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d z} (\frac{z - 4}{z + 4})

Wende die Kettenregel an:

\frac{1}{2 \frac{z - 4}{z + 4}} \frac{d}{d z} (\frac{z - 4}{z + 4})

= \frac{1}{2 \frac{z - 4}{z + 4}} \frac{d}{d z} (\frac{z - 4}{z + 4})

\frac{d}{d z} (\frac{z - 4}{z + 4}) = \frac{8}{( z + 4 ) ^{2}}

= \frac{1}{2 \frac{z - 4}{z + 4}} \cdot \frac{8}{( z + 4 ) ^{2}}

Vereinfache

\frac{1}{2 \frac{z - 4}{z + 4}} \cdot \frac{8}{( z + 4 ) ^{2}} : \frac{4}{z - 4 ( z + 4 ) ^{\frac{3}{2}}}

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

\frac{\partial}{\partial x} (x ln (z^{2} + x^{7}))

\frac{d}{d x} (x^{4} e^{- x})

\frac{d}{d x} ((csc (x) + cot (x))^{- 1})

n = 0 \sum \infty - \frac{n}{2}

d er i v a t i v e x^{4} + 6 x^{2} - x