derivative y=(2x+1)^{sin(5x)}

Lösung

ableitung von

y = (2 x + 1)^{s i n (5 x)}

(5 cos (5 x) ln (2 x + 1) + \frac{2 sin ( 5 x )}{2 x + 1}) (2 x + 1)^{s i n (5 x)}

Schritte zur Lösung

\frac{d}{d x} ((2 x + 1)^{s i n (5 x)})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

(2 x + 1)^{s i n (5 x)} = e^{s i n (5 x) l n (2 x + 1)}

= \frac{d}{d x} (e^{s i n (5 x) l n (2 x + 1)})

Wende die Kettenregel an:

e^{s i n (5 x) l n (2 x + 1)} \frac{d}{d x} (sin (5 x) ln (2 x + 1))

= e^{s i n (5 x) l n (2 x + 1)} \frac{d}{d x} (sin (5 x) ln (2 x + 1))

\frac{d}{d x} (sin (5 x) ln (2 x + 1)) = 5 cos (5 x) ln (2 x + 1) + \frac{2 sin ( 5 x )}{2 x + 1}

= e^{s i n (5 x) l n (2 x + 1)} (5 cos (5 x) ln (2 x + 1) + \frac{2 sin ( 5 x )}{2 x + 1})

e^{s i n (5 x) l n (2 x + 1)} = (2 x + 1)^{s i n (5 x)}

= (5 cos (5 x) ln (2 x + 1) + \frac{2 sin ( 5 x )}{2 x + 1}) (2 x + 1)^{s i n (5 x)}

d er i v a t i v e \frac{5}{3 x ^{2}}

d er i v a t i v e y = lo g_{10} (3 x)

d er i v a t i v e f (x) = (1 + 2 e^{x}) sin (x)

d er i v a t i v e - 2^{x}

d er i v a t i v e \frac{1}{4} \cdot x^{2} - \frac{( sin ( 2 x ^{2} ) )}{8}