(\partial)/(\partial x)(3(((4+z))/(5+x))^2)

Lösung

\frac{\partial}{\partial x} (3 (\frac{( 4 + z )}{5 + x})^{2})

- \frac{6 ( 4 + z ) ^{2}}{( 5 + x ) ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (3 (\frac{( 4 + z )}{5 + x})^{2})

Behandle

z

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} ((\frac{4 + z}{5 + x})^{2})

Wende die Kettenregel an:

2 \cdot \frac{4 + z}{5 + x} \frac{\partial}{\partial x} (\frac{4 + z}{5 + x})

= 2 \cdot \frac{4 + z}{5 + x} \frac{\partial}{\partial x} (\frac{4 + z}{5 + x})

\frac{\partial}{\partial x} (\frac{4 + z}{5 + x}) = - \frac{4 + z}{( 5 + x ) ^{2}}

= 3 \cdot 2 \cdot \frac{4 + z}{5 + x} (- \frac{4 + z}{( 5 + x ) ^{2}})

Vereinfache

3 \cdot 2 \cdot \frac{4 + z}{5 + x} (- \frac{4 + z}{( 5 + x ) ^{2}}) : - \frac{6 ( 4 + z ) ^{2}}{( 5 + x ) ^{3}}

= - \frac{6 ( 4 + z ) ^{2}}{( 5 + x ) ^{3}}

d er i v a t i v e e^{x} - x^{5}

n = 1 \sum \infty 2^{n} \frac{1}{n ^{2}}

\int \frac{x ^{2}}{144 - x ^{2}} d x

\int_{3}^{32} \frac{1}{x ^{3} - 27} d x

t an g e n t f (x) = \frac{5 x}{x + 3}, at x = 2