derivative h(x)=(xtan(x))^7

Lösung

ableitung von

h (x) = (x tan (x))^{7}

7 x^{6} tan^{7} (x) + 7 tan^{6} (x) sec^{2} (x) x^{7}

Schritte zur Lösung

\frac{d}{d x} ((x tan (x))^{7})

Vereinfache

(x tan (x))^{7} : x^{7} tan^{7} (x)

= \frac{d}{d x} (x^{7} tan^{7} (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{7}, g = tan^{7} (x)

= \frac{d}{d x} (x^{7}) tan^{7} (x) + \frac{d}{d x} (tan^{7} (x)) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

\frac{d}{d x} (tan^{7} (x)) = 7 tan^{6} (x) sec^{2} (x)

= 7 x^{6} tan^{7} (x) + 7 tan^{6} (x) sec^{2} (x) x^{7}

\int x sin (a x) d x

\int ln (cos (x)) d x

y^{^{'}} = 1 - \frac{y}{100}

t an g e n t sin (x)

d er i v a t i v e 5 (x^{2 n - 1}) \cdot (2 x^{3 n + 1})^{2}