derivative of ((2x+5^{3/2})/3)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (2 x + 5) = 2

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

Vereinfache

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

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

\int sec (x) tan (x) sin (sec (x)) d x

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

\frac{d}{d x} (\frac{x - 1}{x + 1})

\frac{d}{d x} (\frac{x y z}{x ^{2} + y ^{2} + z ^{2}})

x \to 5 lim (- x^{2} + 5 x - 8)