derivative of cos(2y-3x^2y^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (cos (2 y)) = - sin (2 y) \cdot 2 \frac{d y}{d x}

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

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

\int x (x^{2} + 5)^{3} d x

\int_{0}^{1} \frac{1}{( x ^{2} + 1 ) ^{2}} d x

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

d er i v a t i v e (arctan (8 x))^{2}

\int_{1}^{e^{2}} ln (x) d x