derivative of (x^2+2x+2^{sin(x)})

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

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

Wende die Kettenregel an:

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

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

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

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

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

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

y^{^{'}} + y = x y^{4}

x \to \infty lim (3 + \frac{2}{x})

f (y) = y

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

\int sec^{4} (2 x) d x