derivative of 2y-1/x+cos(3x)

Lösung

\frac{d}{d x} (2 y - \frac{1}{x} + cos (3 x))

2 \frac{d y}{d x} + \frac{1}{x ^{2}} - 3 sin (3 x)

Schritte zur Lösung

\frac{d}{d x} (2 y - \frac{1}{x} + cos (3 x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 y) - \frac{d}{d x} (\frac{1}{x}) + \frac{d}{d x} (cos (3 x))

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

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= 2 \frac{d y}{d x} - (- \frac{1}{x ^{2}}) - sin (3 x) \cdot 3

Vereinfache

= 2 \frac{d y}{d x} + \frac{1}{x ^{2}} - 3 sin (3 x)

\int x^{2} \cdot cos (mπ x) d x

\frac{d}{d x} (- \frac{1}{( 5 + x ) ^{2}})

x \to 0 lim (2 x^{2} - 10 x + 12)

\int sin (2 x + 3) d x

\int_{0}^{1} (x^{2} + 8) e^{- x} d x