derivative of tan(xsin(x))

Lösung

\frac{d}{d x} (tan (x) sin (x))

sin (x) (1 + sec^{2} (x))

Schritte zur Lösung

\frac{d}{d x} (tan (x) sin (x))

Wende die Produktregel an:

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

f = tan (x), g = sin (x)

= \frac{d}{d x} (tan (x)) sin (x) + \frac{d}{d x} (sin (x)) tan (x)

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

\frac{d}{d x} (sin (x)) = cos (x)

= sec^{2} (x) sin (x) + cos (x) tan (x)

Vereinfache

sec^{2} (x) sin (x) + cos (x) tan (x) : sin (x) (1 + sec^{2} (x))

= sin (x) (1 + sec^{2} (x))

d er i v a t i v e 4 x e^{x}

\frac{\partial}{\partial y} (4 x^{2} + y^{2} - 800)

t an g e n t f (x) = x^{3} - 8 x^{2}, at x = 0

\int sec^{6} (x) tan^{5} (x) d x

x \to 0 lim (\frac{x ^{2}}{2})