derivative (b/(a+z^2))^4

Lösung

ableitung von

(\frac{b}{a + z ^{2}})^{4}

- \frac{8 b ^{4} z}{( a + z ^{2} ) ^{5}}

Schritte zur Lösung

\frac{d}{d z} ((\frac{b}{a + z ^{2}})^{4})

Wende die Kettenregel an:

4 (\frac{b}{a + z ^{2}})^{3} \frac{d}{d z} (\frac{b}{a + z ^{2}})

= 4 (\frac{b}{a + z ^{2}})^{3} \frac{d}{d z} (\frac{b}{a + z ^{2}})

\frac{d}{d z} (\frac{b}{a + z ^{2}}) = - \frac{2 b z}{( a + z ^{2} ) ^{2}}

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

Vereinfache

4 (\frac{b}{a + z ^{2}})^{3} (- \frac{2 b z}{( a + z ^{2} ) ^{2}}) : - \frac{8 b ^{4} z}{( a + z ^{2} ) ^{5}}

= - \frac{8 b ^{4} z}{( a + z ^{2} ) ^{5}}

\int 9 e^{4 x + e^{4 x}} d x

l a pl a ce t r an s f or m (t - 3)^{2}

\int_{0}^{1} \frac{- 10 y}{e ^{2 y}} d y

x \to 0 + lim ((x) (e^{\frac{1}{x}}))

d er i v a t i v e f (x) = 12 x^{2} - 36 x