derivative of x^3+ky(x^2-5xy)

Lösung

\frac{d}{d x} (x^{3} + k y (x) (x)^{2} - 5 x y (x))

3 x^{2} + k (\frac{d}{d x} (y (x)) x^{2} + 2 x y (x)) - 5 (y (x) + x \frac{d}{d x} (y (x)))

Schritte zur Lösung

\frac{d}{d x} (x^{3} + k y (x) (x)^{2} - 5 x y (x))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (k y (x) x^{2}) - \frac{d}{d x} (5 x y (x))

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

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

\frac{d}{d x} (5 x y (x)) = 5 (y (x) + x \frac{d}{d x} (y (x)))

= 3 x^{2} + k (\frac{d}{d x} (y (x)) x^{2} + 2 x y (x)) - 5 (y (x) + x \frac{d}{d x} (y (x)))

t an g e n t \frac{16 x}{x ^{2} + 16}, at - 2, - \frac{8}{5}

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

\int \frac{2 - x ^{2}}{x} d x

t a y l or x e^{x}, 0

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