derivative of ((sqrt(2x+1)/(e+1))^e)

Lösung

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

\frac{e ( 2 x + 1 ) ^{\frac{e - 2}{2}}}{( e + 1 ) ^{e}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{2 x + 1}{e + 1}) = \frac{1}{( e + 1 ) 2 x + 1}

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

Vereinfache

e (\frac{2 x + 1}{e + 1})^{e - 1} \frac{1}{( e + 1 ) 2 x + 1} : \frac{e ( 2 x + 1 ) ^{\frac{e - 2}{2}}}{( e + 1 ) ^{e}}

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

\int_{0}^{5} ∣ x - 2 ∣ d x

\int_{0}^{9} \frac{1}{( x - 1 ) ^{\frac{1}{3}}} d x

\frac{d}{d x} (a x sin (4 x) + b x cos (4 x))

f^{^{'}} (t) - f (t) = 2 t

x \to 3 + lim (\frac{- x}{x - 3})