derivative of sin(xsin(y)sin(x+y))

Lösung

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

cos (x) sin (y) sin (x + y) + (cos (y) \frac{d y}{d x} sin (x + y) + cos (x + y) (1 + \frac{d y}{d x}) sin (y)) sin (x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (sin (y) sin (x + y)) = cos (y) \frac{d y}{d x} sin (x + y) + cos (x + y) (1 + \frac{d y}{d x}) sin (y)

= cos (x) sin (y) sin (x + y) + (cos (y) \frac{d y}{d x} sin (x + y) + cos (x + y) (1 + \frac{d y}{d x}) sin (y)) sin (x)

x \to 2 lim (x^{3} f (x))

n = 1 \sum \infty \frac{( - 1 ) ^{n}}{5 ( 2 ^{n + 2} )}

x \to 1 + lim (\frac{7}{1 - x})

d er i v a t i v e y = 4 - 3 x

\frac{\partial}{\partial x} (e^{- 2 x} cos (8 y))