(\partial)/(\partial y)(ysin(x+y))

Lösung

\frac{\partial}{\partial y} (y sin (x + y))

sin (x + y) + y cos (x + y)

Schritte zur Lösung

\frac{\partial}{\partial y} (y sin (x + y))

Behandle

x

als Konstante

Wende die Produktregel an:

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

f = y, g = sin (x + y)

= \frac{\partial}{\partial y} (y) sin (x + y) + \frac{\partial}{\partial y} (sin (x + y)) y

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

\frac{\partial}{\partial y} (sin (x + y)) = cos (x + y)

= 1 \cdot sin (x + y) + cos (x + y) y

Vereinfache

= sin (x + y) + y cos (x + y)

\frac{d}{d x} (e^{6 x} ln (x^{2} - 4))

\int_{- 1}^{2} (x - 6 ∣ x ∣) d x

\int \frac{1}{- x ^{2} + 6 x - 5} d x

4 x^{3} y + x^{4} y^{^{'}} = sin^{3} (\frac{x}{9})

t a y l or ln (x + 1), 0