derivative y=sin(x)tan(x)

Lösung

ableitung von

y = sin (x) tan (x)

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (3 cos^{4} (x))

a re a (2, 8), y = 2 x^{2}

\frac{d}{d x} (r (t, x) cos (t))

x \to 0 lim (\frac{1 - cos ( 4 x )}{x tan ( 3 x )})

\frac{\partial}{\partial x} (- 2 e^{- 7 x y})