derivative of y^2-2ycos(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

a re a y = 10 x^{4} - 10 x^{2}, y = 9 x^{2}

\int 1 + (cos (x))^{2} d x

\int_{0}^{2} \frac{3}{4 x ^{2} + 5 x + 1} d x

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

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