(\partial)/(\partial x)(sin^2(2x+3y))

Lösung

\frac{\partial}{\partial x} (sin^{2} (2 x + 3 y))

4 sin (2 x + 3 y) cos (2 x + 3 y)

Schritte zur Lösung

\frac{\partial}{\partial x} (sin^{2} (2 x + 3 y))

Behandle

y

als Konstante

Wende die Kettenregel an:

2 sin (2 x + 3 y) \frac{\partial}{\partial x} (sin (2 x + 3 y))

= 2 sin (2 x + 3 y) \frac{\partial}{\partial x} (sin (2 x + 3 y))

\frac{\partial}{\partial x} (sin (2 x + 3 y)) = cos (2 x + 3 y) \cdot 2

= 2 sin (2 x + 3 y) cos (2 x + 3 y) \cdot 2

Vereinfache

= 4 sin (2 x + 3 y) cos (2 x + 3 y)

\int_{0}^{1} x^{2} (x^{3} - 2)^{3} d x

\frac{\partial}{\partial x} (\frac{t}{x})

\frac{d y}{d x} + (\frac{3}{x}) y = - 4 x - 10

\int \frac{1}{x ^{2} - 4} d x

\frac{d y}{d x} = \frac{2}{x}