(\partial)/(\partial x)(sqrt(R(x)^2+x^2)-x)

Lösung

\frac{\partial}{\partial x} (R (x) (x)^{2} + x^{2} - x)

\frac{x \frac{\partial}{\partial x} ( R ( x ) ) + 2 R ( x ) + 2}{2 R ( x ) + 1} - 1

Schritte zur Lösung

\frac{\partial}{\partial x} (R (x) (x)^{2} + x^{2} - x)

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (R (x) x^{2} + x^{2}) - \frac{\partial}{\partial x} (x)

\frac{\partial}{\partial x} (R (x) x^{2} + x^{2}) = \frac{x \frac{\partial}{\partial x} ( R ( x ) ) + 2 R ( x ) + 2}{2 R ( x ) + 1}

\frac{\partial}{\partial x} (x) = 1

= \frac{x \frac{\partial}{\partial x} ( R ( x ) ) + 2 R ( x ) + 2}{2 R ( x ) + 1} - 1

d er i v a t i v e f (0) = (x^{4} + 3 x) (4 x^{5} + 4 x - 2)

d er i v a t i v e - \frac{2}{x ^{2}}

d er i v a t i v e y = ln (\frac{x - 3}{x + 3})

\int (y^{5} - 5 y) d y

t a y l or e^{s i n (x)}