derivative of (x^4+2^{cos(x)})

Lösung

\frac{d}{d x} ((x^{4} + 2)^{c o s (x)})

(- sin (x) ln (x^{4} + 2) + \frac{4 x ^{3} cos ( x )}{x ^{4} + 2}) (x^{4} + 2)^{c o s (x)}

Schritte zur Lösung

\frac{d}{d x} ((x^{4} + 2)^{c o s (x)})

Wende Exponentenregel an:

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

(x^{4} + 2)^{c o s (x)} = e^{c o s (x) l n (x^{4} + 2)}

= \frac{d}{d x} (e^{c o s (x) l n (x^{4} + 2)})

Wende die Kettenregel an:

e^{c o s (x) l n (x^{4} + 2)} \frac{d}{d x} (cos (x) ln (x^{4} + 2))

= e^{c o s (x) l n (x^{4} + 2)} \frac{d}{d x} (cos (x) ln (x^{4} + 2))

\frac{d}{d x} (cos (x) ln (x^{4} + 2)) = - sin (x) ln (x^{4} + 2) + \frac{4 x ^{3} cos ( x )}{x ^{4} + 2}

= e^{c o s (x) l n (x^{4} + 2)} (- sin (x) ln (x^{4} + 2) + \frac{4 x ^{3} cos ( x )}{x ^{4} + 2})

e^{c o s (x) l n (x^{4} + 2)} = (x^{4} + 2)^{c o s (x)}

= (- sin (x) ln (x^{4} + 2) + \frac{4 x ^{3} cos ( x )}{x ^{4} + 2}) (x^{4} + 2)^{c o s (x)}

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