derivative xtan(3x^2+4x+1)

Lösung

ableitung von

x tan (3 x^{2} + 4 x + 1)

tan (3 x^{2} + 4 x + 1) + x sec^{2} (3 x^{2} + 4 x + 1) (6 x + 4)

Schritte zur Lösung

\frac{d}{d x} (x tan (3 x^{2} + 4 x + 1))

Wende die Produktregel an:

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

f = x, g = tan (3 x^{2} + 4 x + 1)

= \frac{d x}{d x} tan (3 x^{2} + 4 x + 1) + \frac{d}{d x} (tan (3 x^{2} + 4 x + 1)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (tan (3 x^{2} + 4 x + 1)) = sec^{2} (3 x^{2} + 4 x + 1) (6 x + 4)

= 1 \cdot tan (3 x^{2} + 4 x + 1) + sec^{2} (3 x^{2} + 4 x + 1) (6 x + 4) x

Vereinfache

= tan (3 x^{2} + 4 x + 1) + x sec^{2} (3 x^{2} + 4 x + 1) (6 x + 4)

d er i v a t i v e x^{2} (x + 1)

d er i v a t i v e n + 1

\frac{d}{d s} (2 s)

\frac{d}{d t} (t^{2} - sec (t) + t)

d er i v a t i v e 5 x^{2} + 3 x + 2