derivative y=x^{9cos(x)}

Lösung

ableitung von

y = x^{9 c o s (x)}

9 x^{9 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{9 c o s (x)})

Wende Exponentenregel an:

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

x^{9 c o s (x)} = e^{9 c o s (x) l n (x)}

= \frac{d}{d x} (e^{9 c o s (x) l n (x)})

Wende die Kettenregel an:

e^{9 c o s (x) l n (x)} \frac{d}{d x} (9 cos (x) ln (x))

= e^{9 c o s (x) l n (x)} \frac{d}{d x} (9 cos (x) ln (x))

\frac{d}{d x} (9 cos (x) ln (x)) = 9 (- sin (x) ln (x) + \frac{cos ( x )}{x})

= e^{9 c o s (x) l n (x)} \cdot 9 (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{9 c o s (x) l n (x)} = x^{9 c o s (x)}

= 9 x^{9 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

\int 2 - ∣ x ∣ d x

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