derivative of 1/(sqrt(3x+5))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int_{1}^{2} x d x

\frac{d}{d x} ([x + (x + sin^{2} (x))^{7}]^{4})

\frac{\partial}{\partial x} (cos^{3} (x^{3} y^{8}))

y^{^{''}} + 5 y^{^{'}} + 6 y = 4 e^{- 2 t}

(1 + \frac{3}{y} + x) \frac{d y}{d x} + y = \frac{3}{x} - 1