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

Lösung

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

2 (- 2 x ln (x + y) + y - x)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y^{2} - x^{2}, g = ln (x + y)

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

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

\frac{\partial}{\partial x} (ln (x + y)) = \frac{1}{x + y}

= 2 ((- 2 x) ln (x + y) + \frac{1}{x + y} (y^{2} - x^{2}))

Vereinfache

2 ((- 2 x) ln (x + y) + \frac{1}{x + y} (y^{2} - x^{2})) : 2 (- 2 x ln (x + y) + y - x)

= 2 (- 2 x ln (x + y) + y - x)

d er i v a t i v e 3 x^{2} - x^{3}

\int \frac{1}{4 x ^{2} + 1} d x

\int \frac{1}{y + y} d y

y^{^{'}} = sin (x^{2})

n = 0 \sum \infty \frac{n + 4}{3 n + 2}