derivative 3x^2sin(x)tan(x)

Lösung

ableitung von

3 x^{2} sin (x) tan (x)

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

Schritte zur Lösung

\frac{d}{d x} (3 x^{2} sin (x) tan (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (x^{2} sin (x) tan (x))

Wende die Produktregel an:

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

f = x^{2}, g = sin (x) tan (x)

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

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

\frac{d}{d x} (sin (x) tan (x)) = sin (x) (1 + sec^{2} (x))

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

\frac{d y}{d x} - \frac{y}{x} = 2 x e^{x}, y (1) = 2 e - 8

\frac{d}{d x} (13 9 + 7 5 2 x)

\int (sec^{2} (θ) + sec (θ) tan (θ)) d θ

\frac{d}{d y} (x y)

\frac{\partial}{\partial y} (2 - y - 2 x)