(\partial)/(\partial x)(9xsin(8x^2y))

Lösung

\frac{\partial}{\partial x} (9 x sin (8 x^{2} y))

9 (sin (8 x^{2} y) + 16 x^{2} y cos (8 x^{2} y))

Schritte zur Lösung

\frac{\partial}{\partial x} (9 x sin (8 x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 9 \frac{\partial}{\partial x} (x sin (8 x^{2} y))

Wende die Produktregel an:

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

f = x, g = sin (8 x^{2} y)

= 9 (\frac{\partial}{\partial x} (x) sin (8 x^{2} y) + \frac{\partial}{\partial x} (sin (8 x^{2} y)) x)

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (sin (8 x^{2} y)) = cos (8 x^{2} y) \cdot 16 y x

= 9 (1 \cdot sin (8 x^{2} y) + cos (8 x^{2} y) \cdot 16 y xx)

Vereinfache

9 (1 \cdot sin (8 x^{2} y) + cos (8 x^{2} y) \cdot 16 y xx) : 9 (sin (8 x^{2} y) + 16 x^{2} y cos (8 x^{2} y))

= 9 (sin (8 x^{2} y) + 16 x^{2} y cos (8 x^{2} y))

l a pl a ce t r an s f or m e^{3 t} cos (2 t)

\frac{d}{d x} (sin^{2} (e^{s i n^{2} (x)}))

\int 3 x cos^{3} (x^{2} + 2) d x

t an g e n t f (x) = x^{2}, at m (x) = - \frac{1}{2}

\frac{d}{d x} (r^{2} - 8 x^{2})