derivative of y^3+xy^2+y+xcos(3x-2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\frac{d}{d x} (2) = 0

= 3 y^{2} \frac{d y}{d x} + y^{2} + 2 x y \frac{d y}{d x} + \frac{d y}{d x} + cos (3 x) - 3 x sin (3 x) - 0

Vereinfache

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

\frac{d}{d x} (\frac{( x ^{2} - 4 )}{x - 2})

d er i v a t i v e \frac{1 + X}{1 - X}

\int e^{c o s (25 t)} sin (25 t) d t

t an g e n t x + \frac{5}{x}

\frac{x d y}{d x} - y = x^{2017} \cdot y^{2}