(\partial)/(\partial x)(x+3*ln(x)-y^2)

Lösung

\frac{\partial}{\partial x} (x + 3 \cdot ln (x) - y^{2})

\frac{3}{x} + 1

Schritte zur Lösung

\frac{\partial}{\partial x} (x + 3 ln (x) - y^{2})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (3 ln (x)) - \frac{\partial}{\partial x} (y^{2})

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

\frac{\partial}{\partial x} (3 ln (x)) = \frac{3}{x}

\frac{\partial}{\partial x} (y^{2}) = 0

= 1 + \frac{3}{x} - 0

Vereinfache

= \frac{3}{x} + 1

\frac{d}{d x} (a x^{2} + x)

\int_{5}^{6} \frac{1}{x ^{2} - 1} d x

\int_{- 2}^{3} \frac{18}{x ^{4}} d x

d er i v a t i v e x^{2} + 7

\frac{\partial}{\partial x} (3 x^{2} + 5 y^{3})