derivative of (x^2+3^{sin(x)})

Lösung

\frac{d}{d x} ((x^{2} + 3)^{s i n (x)})

(cos (x) ln (x^{2} + 3) + \frac{2 x sin ( x )}{x ^{2} + 3}) (x^{2} + 3)^{s i n (x)}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 3)^{s i n (x)})

Wende Exponentenregel an:

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

(x^{2} + 3)^{s i n (x)} = e^{s i n (x) l n (x^{2} + 3)}

= \frac{d}{d x} (e^{s i n (x) l n (x^{2} + 3)})

Wende die Kettenregel an:

e^{s i n (x) l n (x^{2} + 3)} \frac{d}{d x} (sin (x) ln (x^{2} + 3))

= e^{s i n (x) l n (x^{2} + 3)} \frac{d}{d x} (sin (x) ln (x^{2} + 3))

\frac{d}{d x} (sin (x) ln (x^{2} + 3)) = cos (x) ln (x^{2} + 3) + \frac{2 x sin ( x )}{x ^{2} + 3}

= e^{s i n (x) l n (x^{2} + 3)} (cos (x) ln (x^{2} + 3) + \frac{2 x sin ( x )}{x ^{2} + 3})

e^{s i n (x) l n (x^{2} + 3)} = (x^{2} + 3)^{s i n (x)}

= (cos (x) ln (x^{2} + 3) + \frac{2 x sin ( x )}{x ^{2} + 3}) (x^{2} + 3)^{s i n (x)}

l a pl a ce t r an s f or m e^{3 t} (9 - 4 t + 10 sin (\frac{t}{2}))

x \to 0 + lim (x ln (e^{x} - 1))

d er i v a t i v e f (x) = \frac{x ^{2} - 99}{x - 10}

f (x) = e^{5 x^{2}}

\frac{d y}{d x} = 2 y + x^{2} + 7