derivative x^{7cos(x)}

Lösung

ableitung von

x^{7 c o s (x)}

7 x^{7 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Schritte zur Lösung

\frac{d}{d x} (x^{7 c o s (x)})

Wende Exponentenregel an:

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

x^{7 c o s (x)} = e^{7 c o s (x) l n (x)}

= \frac{d}{d x} (e^{7 c o s (x) l n (x)})

Wende die Kettenregel an:

e^{7 c o s (x) l n (x)} \frac{d}{d x} (7 cos (x) ln (x))

= e^{7 c o s (x) l n (x)} \frac{d}{d x} (7 cos (x) ln (x))

\frac{d}{d x} (7 cos (x) ln (x)) = 7 (- sin (x) ln (x) + \frac{cos ( x )}{x})

= e^{7 c o s (x) l n (x)} \cdot 7 (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{7 c o s (x) l n (x)} = x^{7 c o s (x)}

= 7 x^{7 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

x \to 6 lim (2 x + 4)

d er i v a t i v e 8 x - 2 x

x \to π lim (csc (x))

in v erse l a pl a ce x^{2} - 5

t an g e n t f (x) = \frac{3}{x}, at x = a